Admissible Edge-dependent Average Dwell Time Research Articles

Input-to-state stability of impulsive switched systems under mode-dependent event-triggered impulsive control

This paper aims to investigate input-to-state stability (ISS) of nonlinear impulsive switched systems under mode-dependent event-triggered impulsive control (MDETIC) method. A novel mode-dependent event-triggered mechanism (MDETM) is devised, where triggering impulsive instants are determined by some predesigned event conditions. Different from existing MDETM, there are two types of impulsive behavior involved, including the impulsive behavior of system itself and event-triggered one. The novel MDETM not only reduces communication cost and energy consumption but also excludes “Zeno behavior.” Then, the ISS criteria of the closed-loop system are established based on MDETIC strategy, admissible edge-dependent average dwell time (AED-ADT), and admissible edge-dependent average impulsive interval (AED-AII) methods. Finally, two examples are given to verify the effectiveness of the main results.

Input-to-state stability of discrete-time impulsive switched delayed systems with delay-dependent impulse under two asynchronous cases

This paper studies a class of discrete-time impulsive switched delayed systems with delay-dependent impulses, aiming to solving the input-to-state stability (ISS) problem in the case of asynchronous switching signal between subsystem and controller and asynchrony of switching signals and impulsive signals. Among them, the delay effect is handled by a new Lyapunov-Krasovskii function divided into a delay-dependent part and a delay-independent part. In contrast to admissible edge-dependent average dwell time (AED-ADT) methods that address switching signals, we propose admissible edge-dependent average impulsive interval (AED-AII) to deal with delayed impulses, thereby establishing the relationship between these methods and the decay rate. Meanwhile, a stabilizing controller for discrete impulsive switched linear delayed systems is proposed and the minimum average dwell time and controller gain are obtained. Compared with the previous work, the parameters of Lyapunov functional relation depend on the directed edges; the operation of subsystem is divided into asynchronous time and synchronous time, which are less conservative; the combination of AED-ADT and AED-AII can be applied to a wider range of impulsive switched systems. Finally, two examples are given to show the effectiveness of the results.

Exponentially Synchronous Results for Delayed Neural Networks With Leakage Delay via Switched Delay Idea and AED-ADT Method.

Time delay has always been one of the main factors affecting the application performance of neural network (NN) systems, and dynamic performance research of NNs with time delays has been the focus of many scholars in recent years. This article enquires into the exponentially synchronous problem of switched delayed NNs with time delay in the leakage term. Adopting an unusual form from a common switched system, the switching modes of the switched delayed NNs system in this article are dependent on time delays. In the first place, the master, slave, and error NNs models are reconstructed into the switched form by introducing the switched delay idea. Then with the help of the admissible edge-dependent average dwell time (AED-ADT) method and delay-dependent switching adjustment indicators, a novel set of generalized delay-mode-dependent multiple Lyapunov-Krasovskii functionals (MLKFs) is built for analyzing the cases where a state-feedback controller exists and does not exist in the model, and where parts of LKFs may increase during the period when the corresponding subsystems are activated. For these cases, several effective exponential synchronization criteria and switching laws are presented accordingly. At last, the verification of the theoretical results is shown through a few examples.

Event-Triggered Adaptive Tracking With Guaranteed Transient Performance for Switched Nonlinear Systems Under Asynchronous Switching.

This article presents an event-triggered neural-network (NN) tracking control scheme, capable of ensuring transient performance for switched nonlinear systems. A mode-dependent event-triggered communication mechanism (MDETCM) is designed, and this significantly saves communication resources without limiting the number of switches between two consecutive triggering instants. Meanwhile, to solve the impact of asynchronous switching on system performance, the information of the switching signal is considered into the event-triggered mechanism (ETM). Also, by introducing a normalized function transformation and a tan-type barrier function, the transient performance is regarded as a tracking error constraint without considering the initial conditions of system output and reference signal required in traditional prescribed performance bound (PPB) control. At the same time, the improved admissible edge-dependent average dwell time (AED-ADT) method is cleverly connected with adaptive backstepping control, and a state-feedback tracking algorithm is proposed, under which all closed-loop signals are bounded and the transient performance of the controlled plant is ensured. Finally, the superiority of the proposed scheme is demonstrated through numerical studies, and the control scheme is available for a single-link robot.

Asynchronous finite‐time dynamic output feedback control for discrete‐time switched linear systems with admissible edge‐dependent average dwell time

AbstractThis paper is concerned with the problem of asynchronous finite‐time dynamic output feedback (DOF) control for a class of discrete‐time switched linear systems under the admissible edge‐dependent average dwell time (AED‐ADT) switching scheme. The main goal of the paper is to design a DOF controller to ensure that the resulting closed‐loop system is finite‐time bounded with AED‐ADT switching and has a specific performance. Firstly, some new sufficient conditions for stability criterion and performance analysis are established based on the multiple Lyapunov functionals technique and the linear matrix inequalities method. Secondly, a type of DOF controllers that guarantee that the closed‐loop system has desired performance is designed. Finally, the effectiveness of the proposed approaches is elaborated with a numerical example.

An Exponential Stabilization Analysis for Switched Interval Type-2 Fuzzy Sampled-Data Control Systems

This work is focused on designing the admissible edge-dependent average dwell time (AE-DADT) based fuzzy sampled-data control problem for a class of switched nonlinear systems. The upper and lower grade of membership functions is used to characterize uncertain parameter-dependent nonlinear systems in the interval type-2 fuzzy (IT2F) model. Unlike from the existing literature, a new fuzzy dependent refined looped-Lyapunov functional (LF) is introduced which involves the new exponent terms and state information such as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\frac{e^{2\gamma _{v}(\varrho -\varrho _{\mathscr {k}})}-1}{2\gamma _{v}}, \ \frac{e^{2\gamma _{v}(\varrho _{\mathscr {k}+1}-\varrho)}-1}{2\gamma _{v}}, \ \mathscr {z}(\varrho _{\mathscr {k}})$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {z}(\varrho _{\mathscr {k}+1})$</tex-math></inline-formula> with tuning parameters and few slack variables. The AE-DADT switching property has also been taken into account for nonlinear systems, and it contributes to getting more information about previous modes. Based on the proposed new refined looped-LFs, new sufficient conditions are derived in terms of linear matrix inequalities (LMI), which ensure the global uniform exponential stability (GUES) of the nominated switched IT2F systems. The feasibility of the obtained results is verified by the numerical example, and the tunnel diode circuit system model and Lorenz chaotic system are established to illustrate the feasibility and efficacy of the theoretical findings.

Adaptive Fuzzy Inverse Optimal Control of Nonlinear Switched Systems

Existing approaches to optimal control for uncertain switched systems require heavy computations for approximating and learning the optimal solution of the Hamilton—Jacobi—Bellman equation. To overcome this problem, a fuzzy adaptive inverse optimal control strategy is first developed for switched systems, which minimizes the cost functional but circumvents solving the Hamilton—Jacobi—Bellman equation. Specifically, an alternative practical inverse approach is developed by two Lyapunov functions method, based on which the inverse optimality regarding a meaningful cost function is achieved. In addition, a new condition of admissible edge-dependent average dwell time is developed by applying the extended multiple Lyapunov functions method. Guided by this weaker condition, the stability of the considered switched system is proved. Finally, simulations are carried out to verify the developed method.

Novel Adaptive Event-Triggered Fuzzy Command Filter Control for Slowly Switched Nonlinear Systems With Constraints.

This article addresses the adaptive fuzzy control problem for switched nonlinear systems with state constraints. The unified barrier function (UBF) is introduced to solve the time-varying state constraints, which removes the feasibility conditions. By integrating command filter into backstepping control to avoid the "explosion of complexity." In addition, a novel event-triggered strategy is designed to deal with the asynchronous switching between subsystems and controllers without limiting the maximum asynchronous time, and mitigate the communication burden. Also, a new threshold function is introduced to overcome the difficulty of discontinuous triggering error at the switching instants. Then, by combining the improved admissible edge-dependent average dwell-time (AED-ADT) method with Lyapunov stability analysis, it is proved that all system signals are bounded and do not violate the predefined constraints under given switching rule. Finally, the numerical simulation results verify the superiority of the proposed algorithm, and the algorithm is applied to a ship maneuvering system.

Unified stability criteria of asynchronous discrete-time impulsive switched delayed systems: bounded admissible edge-dependent average dwell time method

This article investigates input-to-state stability (ISS) problem of asynchronous discrete-time impulsive switched delayed systems, in which switching and impulse may be asynchronous. A novel bounded admissible edge-dependent average dwell time (BAED-ADT) switching signal is designed. Based on this division rule of switching subsystems, we adopt the slow switching method for the stable subsystems and the fast switching method for the unstable subsystems, so that stable subsystems can compensate unstable subsystems. Combined with admissible edge-dependent average impulsive interval (AED-AII) impulsive signal, a new unified ISS stability result is established, which could be applied to impulsive switched systems with an arbitrary combination of unstable and stable subsystems. Without solving the linear matrix inequality, it is allowed to readjust the AED-ADT boundary of the newly proposed stability condition according to the actual impulsive and switching signal. Further, compared with the existing fruits, the new stability condition is an extension and improvement of the previous one, which is less conservative. Several numerical examples are provided to show the validity of the conditions and the advantages of the theoretic results.

Composite event‐triggered H∞ control for nonlinear switched singular systems with a mode‐dependent triggering strategy

SummaryThis paper considers the event‐triggered control problem of nonlinear switched singular systems (NSSSs) with incremental quadratic constraints (IQCs) via a mode‐dependent hybrid triggering strategy. First, impulsive control is introduced to reduce the effect of impulse caused by switching, and the closed‐loop system is modeled as an impulsive NSSS. Then, a novel mode‐dependent hybrid event‐triggering strategy (ETS) consisting of disturbance‐influenced ETS and Lyapunov‐function‐dependent ETS is constructed to avoid Zeno behavior and asynchronous phenomena. Based on this ETS and admissible edge‐dependent average dwell time (AED‐ADT) method, some new sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that the closed‐loop system is regular, impulse‐free, has a unique solution, and is globally uniformly asymptotically stable (GUAS) with a weighted performance. Further, Zeno behavior is excluded by calculating the minimum lower bound of inter‐event time. Finally, a numerical example and a practical application are proposed to demonstrate the validity of the results.

Finite-time H∞ control under the Round-Robin protocol for switched linear systems with admissible edge-dependent average dwell time

This article focuses on finite-time [Formula: see text] control under the Round-Robin protocol for switched linear systems with admissible edge-dependent average dwell time. To relieve the bandwidth pressure of the sensor, a Round-Robin protocol is constructed to decide the access rights of each node of the sensor. Under the Round-Robin protocol-based control structure, admissible edge-dependent average dwell time is applied to describe the transition relationship between the modes of the subsystem and release the restrictions of mode-dependent average dwell time. Moreover, the finite-time stability and [Formula: see text] performance of switched system with Round-Robin protocol are analyzed by using multiple Lyapunov function method combined with the admissible edge-dependent average dwell time switching. Sufficient conditions for the solution to finite-time control problem are derived which consider the [Formula: see text] performance index. Finally, the availability of the control synthesis methods is verified by the circuit model of Buck–Boost converter.

Adaptive Fuzzy Output-Feedback Predefined-Time Control of Nonlinear Switched Systems With Admissible Edge-Dependent Average Dwell Time

This article investigates the adaptive fuzzy output-feedback predefined-time control of nonlinear switched systems with an admissible edge-dependent average dwell time. Different from most of the existing results on neural or fuzzy adaptive finite/fixed-time tracking control of switched systems, where the tracking error goes to a small neighborhood of the origin within finite time, the proposed one can ensure the output tracking error to reach user-defined accuracy within predefined time, which can be arbitrarily preassigned by the designers. Technically, based on the mode-dependent fuzzy state observer, an adaptive output-feedback predefined-time controller is constructed by incorporating a new state-scale transformation function into the barrier Lyapunov function, ensuring predefined transient behavior and tracking accuracy. Besides, by extending the adaptive control problem to the admissible edge-dependent average dwell time framework, the proposed adaptive control scheme can guarantee that all the closed-loop signals are bounded under switching signals with an admissible edge-dependent average dwell time property. It is less conservative than the average dwell time and mode-dependent average dwell time. Finally, two illustrative examples validate the performance of the method presented.

Finite-time H∞ control of discrete-time switched systems based on transferring-dependent Lyapunov function approach

This paper studies the finite-time issues (finite-time stability, finite-time boundedness, finite-time [Formula: see text] control) of discrete-time switched systems. Different from the existing Lyapunov function (LF) approaches only concerning activated subsystem, a novel approach for constructing LF is first proposed, which not only depends on the subsystem the switching reaches but also is closely related to the freshly inactive subsystem. Based on this, a transferring-dependent convex Lyapunov function (CLF) and a transferring-dependent LF are introduced, under which the improved finite-time stability results are deduced with admissible edge-dependent average dwell time (AED-ADT) technique. In light of the merits of established finite-time stability criteria, two transferring-dependent controllers are devised—that is, transferring-dependent convex controller (TD-CC) and transferring-dependent ordinary controller (TD-OC)—to perform finite-time control synthesis. Then, the finite-time [Formula: see text] control is further investigated based on the obtained control synthesis results. The designed transferring–dependent controllers can guarantee that the underlying system is finite-time bounded (FTB) with a prescribed [Formula: see text] performance under tighter AED-ADT switching signals. Besides, it is the first time to use the multiple convex Lyapunov function (MCLF) to investigate the finite-time issues. Finally, two numerical examples and a practical example are used to verify the effectiveness of the developed results.

Integral input-to-state stability of switched delayed systems with delay-dependent impulses under generalized impulsive and switching scheme

This paper studies integral input-to-state stability (iISS) of a class of hybrid delayed systems with impulse and switching behavior, in which the delay-dependent impulse and switching behavior are allowed for asynchronous occurrence. Relative to admissible edge-dependent average dwell time (AED-ADT) concept of the switching signal, a fresh concept of admissible edge-dependent average impulsive interval (AED-AII) is proposed for the impulse signal. Several sufficient criteria for iISS are achieved by using multiple Lyapunov–Krasovskii functional (MLKF) tool, AED-ADT switching, and AED-AII schemes. An improved inequality that describing the relation among Lyapunov function continuous switching signal and discrete impulse is constructed, where the jump amplitude at discrete switching points and impulsive moments including delay-dependent part and delay-independent part are involved. Compared with existing results, our conclusions have the following novelties: (1) the influence of time delay existing in continuous dynamics and discrete impulse on the function part of L-K functional is dug out, which is less conservative; (2) the AED-AII scheme proposed in this paper is combined with the AED-ADT switching method, which contains a larger set of the impulsive and switching signal. Moreover, the stability criterion is suitable for the arbitrary time delay in situation that all the subsystems are destabilizing. Finally, an example is given to verify the validity of the results.

Admissible edge-dependent finite-time ℋ∞ filtering for discrete-time switched systems with average dwell time

Considering that the property of finite-time convergence is of great significance for practical filters, this article is focused on the finite-time ℋ∞ filtering for discrete-time switched systems with average dwell time. Different from the case of the general mode-dependent switching, the information of the admissible switching edge is fully exploited to derive more preferable filtering scheme. In order to further reduce the design conservatism, the multiple discontinuous Lyapunov function approach, which incorporates the concept of admissible edge-dependent average dwell time, is used to analyze the finite-time stability and ℋ∞ performance of the filtering error system. This approach assigns each subsystem of the error system with a discontinuous function rather than a continuous one, so it is less conservative compared to the conventional multiple Lyapunov function approach. First, the finite-time boundedness and ℋ∞ performance is analyzed for general switched nonlinear systems with admissible edge-dependent average dwell time. Then, a sufficient condition of the finite-time boundedness and ℋ∞ performance is derived for the filtering error system based on the obtained criterion. Subsequently, an admissible edge-dependent finite-time filtering scheme is proposed for the underlying system in terms of linear matrix inequalities. Finally, the proposed filter design scheme is applied to a DC–DC power converter circuit, and its effectiveness and superiority are verified by the simulation results.

Input-to-state stability for impulsive switched systems with delays based on a class of generalised impulsive and switching signals

ABSTRACT The input-to-state stability (ISS) for discrete-time impulsive switched systems with delays is investigated, which contains both stable and unstable subsystems. By utilising the multiple Lyapunov–Krasovskii functionals (MLKFs), the delay effects, which are divided into delay-independent part and delay-dependent part, have been processed. Some sufficient conditions are presented to ensure the ISS of system, provided that the switchings and the impulses do not occur too frequently and the activation time of unstable subsystems is comparatively short. Meanwhile, a relationship is built up among admissible edge-dependent average dwell time (AED-ADT), admissible edge-dependent average impulsive interval (AED-AII), impulses magnitude, and decaying/increasing rates of the Lyapunov function. Contrast to previous works, some improvements are made: the effect of delays are fully explored, and the resulting ISS criteria are available with different impulses; AED-AII is first proposed , and combined with AED-ADT to handle the stability problem. Two numerical examples are given to illustrate the theoretical results.

Dwell-time-dependent memory based state feedback controller design for switched Takagi–Sugeno fuzzy nonlinear systems

This paper presents the memory-based Takagi–Sugeno (T-S) fuzzy state feedback controller (SFC) for switched nonlinear systems based on the admissible edge-dependent average dwell time (AEDADT) rule. Different from the existing studies, the fuzzy dependent exponential Lyapunov–Krasovskii functional (LKF) is introduced for switched nonlinear systems, which include the notion of the derivative of membership functions based on the switching idea. Besides that, when compared to the traditional SFC framework, a time-varying delay is involved with the AEDADT switching rule in control gain matrices that are considered for the first time to tackle the stabilization problem. Further, the AEDADT switching property is considered for proposed nonlinear systems, and it contributes to getting more information about previous modes. Based on the proposed membership function dependent exponential LKF, new sufficient conditions are carried out to stabilize the proposed nonlinear systems in terms of the linear matrix inequalities (LMIs) technique. To support the applicability and efficacy of the proposed controller scheme, the tunnel diode circuit system model is illustrated. Also, the feasibility of the obtained results is verified by the numerical example.

Stochastic input-to-state stability for nonlinear impulsive switched systems with random impulses coupled by multiple jump maps

This article focuses on a class of nonlinear random impulsive and switched systems for stochastic input-to-state stability. The impulse is divided into two types: single jump map and multiple jump maps. When the impulse is chosen as single jump map, it means that the impulse between the two adjacent switching times is single as well as impulse and switching occur simultaneously, in which the impulsive moments are fixed. When the impulse is chosen as multiple jump maps, in this model, the impulse is not only limited by multiple maps, but also the impulse instants are assumed to be random. Therefore, this model is an extension of the traditional impulsive and switched system. In view of admissible edge-dependent average dwell time switching signal and the impulse dynamic satisfying Poisson’s process, sufficient conditions for the stochastic input-to-state stability are introduced into nonlinear impulsive switched system with random impulses. Three significant distinctions from the existing results rest with that (1) a new multiple Lyapunov functions are first created; the novelty contains discontinuity at the discrete points including switching moments and the impulse jump instants of Lyapunov-like functional; (2) the coefficient of derivative of a Lyapunov-like functions is permitted to be either positive or negative, which is less conservative; (3) the adopted admissible edge-dependent average dwell time switching scheme delves into less conservative stochastic input-to-state stability condition than mode-dependent average dwell time switching, nonlinear impulsive switched system with various jump maps. Numerical examples are simulated to manifest the validity of the main results.

Input‐to‐state stability of discrete‐time switched delayed systems with delay‐dependent impulses: Admissible edge‐dependent average impulsive interval

AbstractThis article addresses the input‐to‐state stability (ISS) problem for general discrete‐time impulsive and switched delayed systems coupled by delay‐dependent impulses. In our studied systems, the impulsive signal has a large degree of freedom, that is, the impulse effect can occur simultaneously with or different from the switching effect. A new Lyapunov–Krasovskii functional is proposed to deal with the delay effect of switching signal and impulsive jump, which is divided into the delay‐independent part and delay‐dependent part. A new concept named admissible edge‐dependent average impulsive interval (AED‐AII) is set up to characterize the impulse sequence relative to the admissible edge‐dependent average dwell time (AED‐ADT) concept of the switching signal. Based on AED‐ADT approach and AED‐AII technique, some improved sufficient outcomes guaranteeing ISS of discrete‐time impulsive and switched delayed systems are presented, respectively, for stabilizing and destabilizing delay‐dependent impulses. Meanwhile, the relationship among AED‐AII, AED‐ADT, the jump amplitude of switching signal and impulse signal at their respective discrete points, the decay rate of Lyapunov functional for system dynamics is connected to pursue ISS of the whole system. Compared with previous works, our setups enjoy the following characteristics: it thoroughly digs the influence of time delay existing in impulses and system dynamics on the function part of L‐K functional, which are less conservative relative to other works; the proposed AED‐ADT switching signals and AED‐AII jump signals cover a large set of hybrid systems. Two numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results.

基于异步切换和可容许边依赖平均驻留时间方法的切换线性系统镇定研究

基于异步切换和可容许边依赖平均驻留时间方法的切换线性系统镇定研究