Mode-dependent Average Dwell Time Switching Research Articles

Bumpless transfer control for switched impulsive positive systems with [formula omitted]-gain performance

This paper investigates the problem of bumpless transfer control for switched impulsive positive systems with L1-gain performance. For switched impulsive positive systems, the control bump is brought from both switching behavior and impulsive effects. First, the concept of bumpless transfer performance is proposed by imposing magnitude constraints on the control signal to measure the level of bumpless transfer in the switched impulsive positive system. Then, based on a new class of multiple piecewise-continuous copositive Lyapunov function, a tighter mode-dependent average dwell time switching signal bound and bumpless transfer controller are designed to realize positive property, bumpless transfer and L1-gain performance of the closed-loop systems. Finally, the feasibility and superiority of the proposed control strategy are illustrated by simulations.

Asynchronous control of switched systems with time-delay based on mode-dependent average dwell time

Switched system is a kind of important hybrid system, which is usually composed of finite subsystems and an organization switching rule. In the study of switched system, it is usually default that the subsystem and the sub-controller are switched synchronously. However, in practice, the switching of sub-controller often lags behind the subsystem, resulting in asynchronous switching between subsystem and sub-controller, which affects the stability of the system. To solve this problem, this paper discusses the asynchronous control problem of a class of time-varying delay switched systems based on mode-dependent average dwell time (MDADT). Firstly, by constructing a dynamic output feedback controller and using piecewise Lyapunov function, the sufficient conditions for exponential stability and H∞ performance of the closed-loop switching system are obtained. At the same time, the design algorithm of dynamic output feedback controller is given. Finally, a simulation of a switched system with two subsystems under ADT switching signal and MDADT switching signal is given, and the effectiveness of the proposed method is verified by comparison.

Mean square exponential stability with l2−l∞ gain of discrete-time switched-Markovian jump systems

In this paper, the problem of mean square exponential stability with [Formula: see text] gain is studied for the discrete-time switched-Markovian jump systems, which are composed of a deterministic switched system and a Markovian jump system. The mode-dependent average dwell time method is adopted to design the switching signal for the deterministic switched system, and the Markovian jump property is presented by the Markov chain, which is dependent on the designed mode-dependent average dwell time switching signal. The multiple discontinuous Lyapunov function is constructed to guarantee the mean square exponential stability and [Formula: see text] performance. Furthermore, a novel inequality is established to show the relationship between multiple discontinuous Lyapunov functions and disturbances to derive the [Formula: see text] performance. Finally, two numerical examples and a circuit system are given to demonstrate the effectiveness of the obtained results.

New stability results for discrete-time switched systems under admissible edge-dependent average persistent dwell-time or admissible edge-dependent persistent dwell-time switching

This paper is devoted to the stability analysis of a class of discrete-time switched systems under newly designed switching regularities. The utilized switching is extended from the primitive mode-dependent persistent dwell-time switching. By integrating the existing admissible edge-dependent average dwell-time switching into the mode-dependent persistent dwell-time regime, a novel admissible edge-dependent average persistent dwell-time strategy involving the notion of admissible transition edges is proposed. The integrated admissible edge-dependent average dwell-time switching has been confirmed to be superior to mode-dependent average dwell-time switching. This superiority makes the proposed switching more general than the relaxed mode-dependent persistent dwell-time switching in the literature. Even if the embedded admissible edge-dependent average dwell-time restrictions degrade to admissible edge-dependent dwell-time ones under special parameter settings, the resulting admissible edge-dependent persistent dwell-time switching retains the advantage of admissible transition edges to generalize the original mode-dependent persistent dwell-time switching. Meanwhile, to remove the switching information reliance in the existing multiple convex Lyapunov functions, an improved multiple convex Lyapunov function method is devised. The designed Lyapunov function can be used to implement broader feasible ranges and tighter lower bounds of admissible edge-dependent average persistent dwell-time (or admissible edge-dependent persistent dwell-time). Finally, the validity and efficiency of the presented approaches are illustrated by a three-phase inverter and a numerical example.

Input-to-State Stability of Switched Network Control Systems Under Unknown Deception Attacks.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

Fault-Tolerant Fuzzy Observer-Based Fixed-Time Tracking Control for Nonlinear Switched Systems

This paper focuses on developing an adaptive output feedback fault-tolerant fixed-time tracking control strategy for a class of switched nonlinear systems with non-affine faults. To approximate the unmeasurable states, a mode-dependent state switched fuzzy observer is generated using fuzzy logic systems and a Butterworth low-pass filter. Next, an adaptive fixed-time tracking control strategy is developed by combining dynamic surface technology with the backstepping method. An improved mode-dependent average dwell time switching rule is also introduced to ensure the stability of switched nonlinear systems with unstable subsystems. A stability analysis proves the effectiveness of the proposed control scheme in stabilizing the switched nonlinear system under mode-dependent average dwell time switching, ensuring that the tracking error reaches the residual set within a derived settling time. Finally, a switched resistor-inductor-capacitor circuit example is provided to demon- strate the validity of the proposed strategy.

Event-Triggered Output Quantized H ∞ Control for Uncertain Switched Singular Systems

This paper presents the co-design problem of robust H∞ controller and event-triggered sampling (ETS) scheme for a class of uncertain switched singular systems (SSS) with output quantization. First, the effect of quantization on the closed-loop system (CLS) is modelled as parameter uncertainty. Then, using multiple Lyapunov functions and mode-dependent average dwell time (MDADT) approach, sufficient conditions are derived to guarantee the CLS is regular, impulse-free and E-uniformly ultimately bounded (E-UUB) satisfying robust H∞ performance. Next, based on these conditions, the quantized output controller gains, ETS scheme parameters, and a class of MDADT switching laws are obtained by solving some linear matrix inequalities (LMIs). Finally, the validity and effectiveness of the proposed control strategy are shown by a computer simulation on a load-varying DC motor.

Asynchronous Switching Control of Discrete Time Delay Linear Switched Systems Based on MDADT

Ideally, switching between subsystems and controllers occurs synchronously. In other words, whenever a subsystem requires switching, its corresponding sub-controller will be promptly activated. However, in reality, due to network delays, system detection, etc., the activation of candidate controllers frequently lags, which causes issues with asynchronous switching between controllers and subsystems. This asynchronous switching problem may affect system performance and even make the system unstable because the state between the subsystem and the controller may be inconsistent, resulting in the controller not being able to control the subsystem correctly. To keep the system stable while using asynchronous switching, this work suggests an asynchronous control technique for a class of discrete linear switching systems with time delay based on the mode-dependent average dwell time (MDADT). First, we construct a state feedback controller and establish a closed-loop system. In the asynchronous and synchronous intervals of subsystems and controllers, different Lyapunov functions are selected, and sufficient conditions for exponential stability and the H∞ performance of the closed-loop system under asynchronous switching are obtained. In addition, using the MDADT switching strategy, the relevant parameters of each subsystem are designed and the corresponding state–feedback controller gain matrix can be obtained. Finally, a switching system with three subsystems is shown. The approach is confirmed by simulating it using the average dwell time (ADT) switching strategy and the MDADT switching strategy separately.

Robust predictive control of perturbed switched linear systems with stable and unstable subsystems in the presence of uncertainties

In this article, robust model predictive control is proposed for discrete-time switched linear systems in the presence of external disturbances, model uncertainties and constraints on the states and input. To solve the problem, a mode-dependent average dwell time switching strategy is constructed in controller design procedure, with less limitations than the existing average dwell time switching. Using some mathematical tools, the model predictive control problem is turned into a feasible linear matrix inequality. The control algorithm is presented via two theorems, and the stability analysis is analytically presented, based on multiple Lyapunov function method. Compared with the previous studies, the underlying switched system may consist of stable and unstable subsystems, perturbed by model uncertainties and external disturbances. The simulation results are also given to study the effectiveness of the proposed robust model predictive control algorithm, from a comparison viewpoint.

Stability and Stabilization of Polynomial Fuzzy-Model-Based Switched Nonlinear Systems Under MDADT Switching Signal

This article proposes a novel Lyapunov stability analysis for a class of switched nonlinear systems under the mode-dependent average dwell time (MDADT) switching signals. For the first time, a polynomial fuzzy model is used to describe the nonlinearity of the switched systems instead of a Takagi–Sugeno fuzzy model, which can represent a wider range of nonlinear plants. As existing advanced results are relatively conservative and lead to that tighter bounds on the dwell time are not easy to be obtained, therefore, the stability analysis for switched systems is still quite challenging. In this article, to tackle this problem, by developing a polynomial multiple Lyapunov function (MLF) approach and exploring the feature of the membership functions, relaxed stability conditions are derived for the switched polynomial fuzzy-model-based control systems. In particular, the polynomial MLF is guaranteed radially unbounded by a two-step procedure, making traditional quadratic MLF a specific case, thereby improved stability conditions can be established in the form of sum-of-squares. Moreover, the new algorithm for multivariate Chebyshev membership functions based on linear programming is proposed to introduce the information of membership functions and further relax the stability conditions to obtain tighter bounds on MDADT. Finally, a simulation example demonstrates the effectiveness of the developed techniques.

Asynchronous Control of Switched Discrete-Time Positive Systems With Delay

This article considers the stabilization issue of switched discrete-time positive systems (SDPSs) with delay by using asynchronous control. Combining transition probability (TP) with mode-dependent average dwell time (MDADT), called TP-based MDADT switching, the SDPSs are more practical than classical models with average dwell-time (ADT) switching. With the aid of a co-positive Lyapunov–Krasovskii functional (CLKF), sufficient conditions ensuring the exponential stability almost surely (ES a.s.) of the SDPSs without control is studied, where the mode is not necessary to be stable. After that, a mode-dependent controller with switching delay is designed to stabilize the SDPSs in the case that there are unstable subsystems. An algorithm is provided to design the control gains. It is discovered that the mode in the closed-loop SDPSs is not required to be stable on synchronous and asynchronous switching intervals. Numerical simulations verify the merits of the new results.

Generic Stability Criteria for Switched Nonlinear Systems With Switching-Signal-Based Lyapunov Functions Using Takagi–Sugeno Fuzzy Model

The aim of this article is to establish generic stability conditions for switched nonlinear systems with mode-dependent average dwell-time (MDADT) switching rules via Takagi–Sugeno (T–S) fuzzy modeling, which cover all unstable modes, all stable modes, and partially unstable modes as special cases. Different from traditional multiple and multiple discontinuous Lyapunov function (MDLF) methods, the proposed novel switching-signal-based multiple discontinuous Lyapunov function (SMDLF) approach divides each mode-running interval dynamically according to the actual switching of the system. The developed approach can not only yield less conservative bounds on the MDADT but can also handle all unstable subsystems, which cannot be done by means of the traditional MDLF. A class of SMDLF is constructed for continuous-time switched T–S fuzzy systems, and relaxed stability conditions are presented for the system with both stable and unstable subsystems, using a larger switching signal space. Then, novel stability conditions are deduced for all stable and unstable subsystems in terms of slow and fast MDADT switching signals, respectively. Finally, comparative simulation examples are provided to verify the advantages and effectiveness of the proposed approach.

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.

Stability analysis for nonlinear switched singular systems via T-S fuzzy modeling

The stability for discrete nonlinear switched singular systems with unstable subsystems is investigated. First, by constructing an appropriate multiple discontinuous Lyapunov function, and utilizing the characteristics of mode-dependent average dwell time switching signals, new stability results for nonlinear switched singular system are established. Then, we adopt the T-S fuzzy modeling method to approximate the nonlinear switched singular systems and get general stability conditions in forms of linear matrix inequalities. Compared to the current results, our technique is more flexible and we also get tighter dwell time boundaries. Furthermore, a numerical example demonstrates the effectiveness of the proposed method.

Robust Finite-Time Control of Discrete-Time Switched Positive Time-Varying Delay Systems with Exogenous Disturbance and Their Application

Many practical systems can be modeled in terms of uncertainties, which refer to the differences or errors between actual data and mathematical simulations. However, systems including slight uncertainties and exogenous disturbances may lead to the instability of those systems. Besides, the behavior of systems is preferable to investigate within a prescribed bound over a fixed time interval. Therefore, in this paper, we study a robust finite-time control of discrete-time linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance. A distinctive feature of this research is that the considered systems consist of finite-time bounded subsystems and finite-time unbounded subsystems. A class of quasi-alternative switching signals is validly designed to analyze the mechanism and switching behaviors of the systems among their subsystems. By utilizing a copositive Lyapunov–Krasovskii functional method combined with the slow mode-dependent average dwell time and the fast mode-dependent average dwell time switching techniques, new sufficient conditions containing several symmetric negative-definite matrices are derived to guarantee robust finite-time control of the systems. These results are applied to a water-quality controllability model in streams to the standard level. Finally, the consistent results between the theoretical analysis and the corresponding numerical simulations are shown.

Finite-Time Boundedness of Linear Uncertain Switched Positive Time-Varying Delay Systems with Finite-Time Unbounded Subsystems and Exogenous Disturbance

The problem of finite-time boundedness for a class of linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance is addressed. This characteristic research is that the studied systems include the finite-time bounded subsystems and finite-time unbounded subsystems. Both a slow mode-dependent average dwell time and a fast mode-dependent average dwell time switching techniques are utilized reasonably. And by applying a copositive Lyapunov-Krasovskii functional, novel delay-dependent sufficient criteria are derived to guarantee such systems to be finite-time bounded concerning the given parameters and designed switching signal. Furthermore, new finite-time boundedness criteria of the systems without interval uncertainties are also obtained. Finally, the efficiency of the theoretical results is presented in two illustrative examples.

Adaptive tracking control of switched cyber-physical systems with cyberattacks

This study investigates the problem of adaptive tracking control for switched cyber-physical systems against cyberattacks. A tracking signal is generated using an exogenous system. An adaptive tracking controller is designed to compensate for the attacks and then stabilize the studied systems. A switching signal is constructed using the mode-dependent average dwell time (MDADT) method. By using the multiple Lyapunov function approach, which is associated with the adaptive estimated signal, the closed-loop error systems with cyberattacks are asymptotically stable under the designed adaptive tracking controller and MDADT switching signal, and the system states can asymptotically track the reference signal. Finally, two examples are provided to validate the theoretical results.

Bumpless Transfer Control for Switched Linear Systems and its Application to Aero-Engines

To avoid the bumps of the control signal in the switching instants, this paper proposes a bumpless transfer control method which guarantees the continuous of control signal while keeping the asymptotic stability of the closed-loop system. Firstly, the presented bumpless transfer control method possesses a simple structure and meanwhile not have to redesign sub-controllers, which is easy to implement. Furthermore, the method is appropriate for either stable subsystems or unstable subsystems, and be suitable for either state feedback control or dynamic output feedback control. Moreover, we give the sufficient conditions of asymptotic stability for switched linear systems under bumpless transfer control for four cases. For the original switched system with stable subsystems under state or dynamic output feedback control, the stability conditions under mode-dependent average dwell time switching are derived. For the original switched system with unstable subsystems under state or dynamic output feedback control, which is stabilized by some certain switching laws, the stability conditions under the original switching law are given. Finally, a hardware-in-the-loop simulation of an aero-engine control system is employed to verify the effectiveness and superiority of the proposed method.

Annular finite-time [formula omitted] control of switched fuzzy systems: A switching dynamic event-triggered control approach

This paper addresses the annular finite-time boundedness H∞ control problem for a class of switched fuzzy systems. A novel switching dynamic event-triggered mechanism is proposed to save communication resources; where two different internal variables are designed and change according to a switching manifold. It is proved that the proposed switching dynamic event-triggered mechanism has a larger minimal inter-execution time in comparison with the static one. With a Lyapunov-like function including the internal dynamic variable, a criterion is established to ensure the annular finite-time boundedness H∞ performance. A dynamic event-triggered controller and a set of feasible mode-dependent average dwell time switching signals are co-designed to achieve desired performance. Finally, an example is presented to validate the effectiveness of the proposed method.

Finite-time stabilization of continuous-time switched positive delayed systems

This paper deals with the problems of finite-time stability and stabilization for continuous-time switched positive linear time-delay systems under mode-dependent average dwell time switching signals. First, finite-time stability conditions are established by constructing an multiple piecewise copositive Lyapunov–Krasovskii functional. Then, finite-time stabilization is achieved by designing a state-feedback controller in the form of linear programming. This numerical construction approach proposed for controller cancels the restriction of the multiple piecewise copositive Lyapunov–Krasovskii functional on controllers, which can decrease the conservatism. Finally, two numerical examples are given to show the advantages of our methods.