Mode-dependent Average Dwell Time Research Articles

Stability analysis and stabilization of discrete-time switched nonlinear systems with mode-dependent average dwell time under nested actuator saturation

In this paper, the stability analysis and stabilization of a class of mode-dependent mean residence time-based discrete-time switching nonlinear systems are addressed. More specifically, under the mode-dependent average dwell time (MDADT) switching mode, combined with the practical problem, the nonlinear factor of nested actuator saturation (NAS) is introduced. Firstly, in order to ensure the system stability, based on the parameter-dependent discontinuous switching Lyapunov function and several basic lemmas, a state feedback controller is designed that makes the closed-loop system (CLS) achieve local exponential stability (LES) by solving the optimal problem in terms of linear matrix inequalities (LMIs). Secondly, the system considers the maximum attraction domain that can be achieved by the NAS system under the conditions. The simulation results show the effectiveness of the proposed design method. At the same time, the efficiency of the proposed method is verified via a water tank example.

Novel Stability Criteria of Asynchronously Switched Nonlinear Neutral Time-Delay Systems.

This article investigates the input-to-state stability and integral input-to-state stability for the switched nonlinear neutral systems (SNNSs) with multiple time-varying delays (MTVDs) and asynchronous switching. According to the fact that the switching signals of the controllers and the subsystems are inconsistent, novel stability criteria on the input-to-state stability and integral input-to-state stability properties for SNNSs with MTVDs and the asynchronous switching phenomenon are presented by multiple Lyapunov-Krasovskii functionals, the merging switching signal, and the mode-dependent average dwell time technique. Compared with the existing related works, our results are less conservative. Meanwhile, our proposed works not only investigate the effects of switches and neutral terms on the stability property for SNNSs but also study the case of the systems with MTVDs and asynchronous switching. Finally, two practical examples, including the practical coupled mass-spring-damper-pendulum system, are presented to show the effectiveness of our results.

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.

Delay-dependent exponential stability of highly nonlinear stochastic functional switched systems: an average dwell time approach

The delay-dependent exponential stability of stochastic functional switched systems (SFSSs) with highly nonlinear coefficients is investigated in this paper. By virtue of the mode-dependent average dwell time (MDADT) technique, the existence of global solution and qth moment exponential stability is studied without linear growth condition (LGC). Both of drift and diffusion coefficients have functional terms which can embody many existing delay cases, e.g. constant delay, time-varying delay and distributed delay, etc. By employing common/multiple Lyapunov function method, sufficient delay-dependent stability criteria of qth moment exponential stability are proposed. The MDADT condition reveals the positive role of switching signal in the delay-dependent stability analysis. Finally, an example is given to validate our theoretical results.

Stabilization of Networked Switched Systems Under DoS Attacks.

This article studies the stability issue of networked switched systems (NSSs) under denial-of-service (DoS) attacks. To address this issue, the derived limitations imposed on both the frequency of DoS attacks on each subsystem and the upper limit of attack duration that each subsystem can tolerate are mode-dependent, which is more efficient and flexible than the current results for NSSs. Moreover, we reveal the relationship between the upper bound of the average maximum tolerable attack duration associated with the corresponding subsystem and the actual mode-dependent average dwell time. Furthermore, we identify that the total tolerable DoS attack duration as a percentage of the system runtime in this article can be higher than existing results. Finally, an example is given to demonstrate the effectiveness of our work.

Stability of highly nonlinear stochastic systems with non-random switching signals and multiple delays

The situation of multiple delays often occur in hybrid stochastic systems. In this paper, multiple time-varying delays are considered for highly nonlinear switching stochastic systems. The function of time-varying delays is differentiable, and its derivative is a positive constant less than 1. By the Lyapunov functional method and the mode-dependent average dwell time approach, existence and uniqueness of solution, asymptotic stability and pth moment exponential stability for highly nonlinear switching stochastic multiple delays systems are obtained. Finally, an example is afforded to explicate the effectiveness our theoretical analysis results.

Consensus and attack-decomposition of switched one-sided Lipschitz multi-agent systems via event-triggered intermittent control

This paper considers the exponential consensus of nonlinear switched multi-agent systems (MASs) subject to random attacks. The proposed model is enhanced by introducing the concept of mode-dependent average dwell time (MDADT) and the one-sided Lipschitz (OSL) condition, making it more practical and versatile with relaxed restrictions. Due to the unavailability of direct access to the states of MASs and the vulnerability of their output signals to unknown random attacks, achieving consensus through traditional methods becomes challenging. Hence, a novel attack-decomposition approach is proposed to extract the attack-free output signals from the attacked output signals. Then, the observer is constructed by utilizing attack-free output signals and employed to estimate the states of MASs. A mode-dependent event-triggering mechanism is presented to conserve resources for the observer-controller channels. In order to save control costs, the intermittent control scheme is designed for different switching modes whose control width depends on the minimum dwell time. Finally, an illustrative example is used to showcase the advantages of the theoretical method.

Dynamic output feedback based fault tolerant control for continuous-time switched affine systems via reduced-order observer

In this study, the issue on dynamic output feedback fault-tolerant controller design is addressed for a class of continuous-time switched affine systems in the presence of actuator faults. The existence of affine terms gives rise to the lack of a common equilibrium point and further makes it more difficult to propose the desired output-feedback-based fault-tolerant control scheme. Firstly, the actuator fault estimation is achieved through a reduced-order observer design approach. Then, a kind of dynamic output feedback controller is constructed to perform the fault tolerance goal by utilizing fault estimation information. Moreover, the mode-dependent average dwell time switching constraint is borrowed to avoid the chattering owing to the high-frequency switching. The sufficient conditions with less conservative are derived to guarantee the practical exponential stability of closed-loop system with a prescribed L∞ gain. Finally, both the effectiveness and validity of the designed fault-tolerant control strategy are illustrated via a case study of a buck-boost DC-DC converter.

Dynamic event-triggered asynchronous control for switched T-S fuzzy systems

The H∞ control problem for a class of continuous-time switched Takagi-Sugeno (T-S) fuzzy systems with mode-dependent average dwell time (MDADT) switching rules is the main topic of this article. Firstly, the transmission burden is relieved by efficiently reducing the number of signal transmissions by the application of a revolutionary dynamic event-triggered mechanism (ETM). Secondly, there is a thorough understanding of the dynamic event-triggered, asynchronous control behaviors that exist between the controllers and subsystems. To ensure H∞ performance of the asynchronous switched T-S fuzzy systems, certain appropriate adequate circumstances are derived by using the merged switching signal approach and Lyapunov-like functional (LKF) method. Lastly, a practical and an numerical example demonstrate the viability and implementation of the conclusions gained.

Stability of highly nonlinear neutral stochastic delay system with both stable and unstable subsystems

AbstractThe article addresses the exponentially stable conditions of the highly nonlinear neutral stochastic delayed system (HNNSDS) that contains unstable subsystems apart from stable ones under Markov switching. By the application of the mode‐dependent average dwell time (MDADT) as well as Lyapunov function approach, the general switching condition still satisfies even when the partial Lyapunov coefficients are negative. In addition, the degree of instability is combined with the study of switching signals. On this basis, the case when the system contains only stable subsystems is also investigated. A well‐known switching condition is obtained, establish the foundation of the comparison with more complex cases involving unstable subsystems. The simulation processes are eventually provided to verify rationality of the obtained criteria.

Exponential stability for switched semi‐Markov jump systems with mode‐dependent average dwell time and generally uncertain transition rates

AbstractThis paper investigates the exponential stability in mean square sense for a class of stochastic switched semi‐Markov jump systems (ssSMJS). In this model, a hierarchical control switched regulation is designed, considering the external stochastic disturbances and generally uncertain transition rates (TRs) of the entire system and making the system more general and practical. By using appropriate Lyapunov–Krasovskii functional, linear matrix inequality, Jensen inequality, and mode‐dependent average dwell time (MDADT), sufficient conditions on the exponential stability in mean square sense for ssSMJS are derived. Furthermore, a nonfragile state feedback controller is designed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed criterion.

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.

Stability of impulsive and switched stochastic delay systems via the event-triggered impulsive mechanism

Under the event-triggered impulsive mechanism, this work introduces the pth moment (integral) input-to-state stability (p-(i)ISS) for a general group of impulsive and switched stochastic delay systems. Using the means of mode-dependent average dwell time and mode-dependent average impulsive interval, some sufficient conditions of p-ISS and p-iISS are supplied. By incorporating the input of subsystems and impulses into the triggering functions, two distinct types of event-triggered impulsive constraint is proposed, which is defined as mode-dependent event-triggered impulsive mechanism with input (MDETIMI). Different from the traditional event-triggered impulsive control, two MDETIMI strategy are individually discussed, which one is the supremum of K∞ function of subsystem input and the superposition of impulsive input, and the other is the integral of K∞ function of subsystem input and the superposition of impulsive input. Moreover, it is unveiled that even with the indeterminate derivatives of the Lyapunov functions, the Zeno phenomenon can effectively be avoided by using MDETIMI strategy. Finally, an example shows the effectiveness and practicability of the results.

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.

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.

Reliable finite-frequency H ∞ control for switched systems with actuator faults and mode-dependent average dwell time

This paper deals with the reliable finite-frequency H ∞ control problem for switched systems with actuator faults and mode-dependent average dwell time (MDADT). The objective of designing reliable controllers is to guarantee the stability and robustness of the closed-loop system in the case of actuator faults. The actuator fault is solved using the convex combination method. A finite-frequency H ∞ performance index is first defined in the frequency domain, and then a finite-frequency performance condition is derived by the generalised Kalman-Yakubovi c ˘ -Popov (GKYP) lemma. Combined with the MDADT approach and linear matrix inequality technology, a sufficient condition for the existence of a set of reliable finite-frequency H ∞ controllers is derived. As a comparison, a sufficient condition is also given for the existence of a set of standard finite-frequency H ∞ controllers. Finally, the effectiveness and feasibility of the proposed method are verified using a tilt-rotor aircraft. In addition, simulations and comparisons show that the designed reliable controller can stabilise the system even if actuator faults occur.

Observer‐based dual event‐triggered control for non‐weighted L2$$ {\mathcal{L}}_2 $$‐gain of switched linear systems

AbstractAs everyone knows, strict mode‐dependent event‐triggered mechanism (MDETM) is rarely studied for switched systems due to the difficulty in settling down the relationship between the dwell time (DT) and triggered intervals. This problem is satisfactorily solved by considering the exponential stabilization via observer‐based dual MDETMs in switched linear systems. The dual MDETMs on the sensor‐controller (S‐C) channel and controller‐actuator (C‐A) channel are designed respectively according to mode‐dependent average dwell time (MDADT). The MDETMs on the C‐A channel are generated based on the MDETMs on the S‐C channel, which makes the new control technique strict mode‐dependent and reduces conservatism as much as possible. Furthermore, when there exists external disturbance, a non‐weighted ‐gain with better performance than existing results is given. By studying an augmented system, exponential stabilization is achieved through a new event‐triggered state estimation (ETSE) and dual MDETMs. The observer gain, controller gain, and non‐weighted ‐gain are derived through an effective algorithm. Finally, two numerical examples are given to illustrate the effectiveness of theoretical research.

Asynchronous H∞ output tracking control for uncertain networked switched systems with mode-dependent average dwell time: an event-driven mechanism

This paper considers the problem of event-triggered H ∞ output tracking control for uncertain networked switched systems with both communication constraints and asynchronous switching. A new sampled delay-dependent error tracking uncertain networked switched system is constructed on the basis of event-triggered communication mechanism (ETCM) and the given reference model. By introducing a parameter-dependent Lyapunov–Krasovskii functional and employing the mode-dependent average dwell time (MDADT) method, results on exponential stability and robust H ∞ performance are proposed. Furthermore, the gains of the output tracking controller with matched system mode are obtained by solving a set of linear matrix inequalities (LIMs), at the same time, the parallel results with the mismatched case are also obtained. Simulation results show that the proposed design scheme not only guarantees tracking performance but also saves communication resources effectively.

A bumpless transfer piecewise filtering approach for fault detection of switched linear systems

AbstractThis study focuses on bumpless transfer (BT) fault detection in switched linear systems operating under mode‐dependent average dwell time (MDADT) switching. We propose a piecewise fault detection filter (FDF) inspired by the segmentation concept inherent in the multiple discontinuous Lyapunov function (MDLF) approach. This filter generates a residual signal that effectively minimizes the amplitude of residual bumps, surpassing the performance of traditional non‐piecewise FDFs. We introduce a new definition of residual BT performance, aimed at reducing residual bump amplitude during filter transitions. The goal is to design the piecewise FDF such that the augmented system maintains asymptotic stability with weighted performance, while also meeting the residual BT performance criteria. The feasibility of achieving BT fault detection filtering is established through linear matrix inequalities (LMIs), leveraging the MDLF and MDADT strategies. The efficacy and benefits of the proposed BT piecewise FDF design are demonstrated through simulations on a boost converter.

Observer-based output feedback event-triggered bounded consensus of multi-agent systems under DoS attacks

This paper is concerned with observer-based output feedback event-triggered bounded consensus problem for linear multi-agent systems. The original multi-agent systems are transformed into the switched systems due to DoS attacks, the fast switching is applied to multi-agent systems with DoS attacks, and slow switching is applied to multi-agent systems with no DoS attacks. A novel mode-dependent dynamic event-triggered scheme and a distributed mode-dependent control protocol are proposed by using the relative output, which include some existing results as special cases. It is shown that bounded consensus can be achieved if each agent is both stabilizable and detectable, the appropriate mode-dependent average dwell time and the co-designed feedback matrices are chosen. Two algorithms are also provided to obtain the lower consensus bound. The above results are also extended to undirected topology. Finally, our theoretical results can be verified by two simulation examples.