Stochastic Stability of Discrete-Time Switched Systems with a Random Switching Signal

Li, Kai; Mu, Xiaomin; Wei, Jumei

doi:10.1155/2015/191458

Cited by 4 publications

(10 citation statements)

References 13 publications

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“…This subsection provides a method to estimate the decay rate and decay coefficient for the discrete-time closed-loop system (9), as shown in Theorem 3. Before giving the Theorem 3, we introduce a lemma which will be used hereafter.…”

Section: An Estimation Methods For the Decay Rate And Decay Coefficientmentioning

confidence: 99%

“…5 The common switching mechanisms can be classified into state-dependent switching rule, 6 time-dependent switching rule, average dwell-time switching rule, 7,8 and random switching rule. 9,10 As mentioned in Reference 11, the switched systems with stable subsystems maybe unstable due to improper switching rules; and the switched systems with unstable subsystems can be stable by choosing proper switching rules. Therefore, the choice of the switching rule plays a significant part in the stability analysis and controller design for switched systems.…”

Section: Introductionmentioning

confidence: 99%

“…The researches of switched systems are more challenging than nonswitched systems on account of their abundant and diverse switching rules 5 . The common switching mechanisms can be classified into state‐dependent switching rule, 6 time‐dependent switching rule, average dwell‐time switching rule, 7,8 and random switching rule 9,10 . As mentioned in Reference 11, the switched systems with stable subsystems maybe unstable due to improper switching rules; and the switched systems with unstable subsystems can be stable by choosing proper switching rules.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

Zhu

Wei

et al. 2020

Intl J Robust & Nonlinear

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This article focuses on the collaborative design of a class of discrete-time switched systems with sojourn probabilities. For the purpose of preventing the data collision, the Try-Once-Discard (TOD) protocol is employed to govern the information transmission between sensors and the controller. Moreover, it is worth noting that the values of sojourn probabilities, which are not given ahead, have an effect on the system stability. As a consequence, a novel collaborative design framework is established, in which the sojourn probability and static output-feedback controller are to be designed simultaneously. By considering the effect from the TOD protocol and using the Lyapunov function related to the mode and protocol, a sufficient condition is derived to guarantee the exponential mean square stability of the closed-loop system with a prescribed lower bound on the decay rate. Then, the desired sojourn probabilities and controller gains dependent on the corresponding mode and protocol are obtained in terms of convex optimization method with equality constraints. Subsequently, an estimation approach is provided to estimate the decay rate and decay coefficient of the closed-loop system. Finally, one numerical example is given to testify the effectiveness of the proposed design approach.

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Section: An Estimation Methods For the Decay Rate And Decay Coefficientmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

Zhu

Wei

et al. 2020

Intl J Robust & Nonlinear

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show abstract

“…On the other hand, compared with the Markov chain, the switching signal is capable of modeling the switched systems with the lower bound of the sojourn time, which benefits from the presence of the fixed part. In virtue of the less conservatism in finding the set of admissible switching signals and the generality in modeling more switching cases, it greatly impulses the studies on stability analysis and control synthesis for switched systems with this type of switching signals 15‐19 . However, almost all the existing results require the prior transition probabilities between different modes.…”

Section: Introductionmentioning

confidence: 99%

A class of switched linear systems with persistent sojourn‐time expectation: Analysis and synthesis

Cai

et al. 2023

Intl J Robust & Nonlinear

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This paper is concerned with the problems of stability and stabilization for discrete‐time switched linear systems with a new class of switching signals. The considered switching signals are of random mode‐dependent sojourn‐time (RMST) property, which is capable of describing the mode‐dependent sojourn‐time period consisting of a fixed part with no switching and a random part with known sojourn‐time expectation. Compared with the previous studies assuming that the switching dynamics of the random part can be described by a Markov chain, the length of the random part is allowed to obey any distribution including geometric distribution. Besides, the mode switching of RMST switching is arbitrary indicating that it requires no statistical information of transition probabilities. The criteria of stability and stabilization are derived for the RMST switched systems. To further reduce the limitation of RMST switching on switching frequency, a concept of random mode‐dependent persistent sojourn‐time (RMPST) is proposed. Then, in the presence of asynchronous switching, the conditions of the existence of controllers are presented for the switched systems with persistent sojourn‐time expectation. A numerical example and a practical example of a space robot manipulator are given to demonstrate the effectiveness and applicability of the developed theoretical results.

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“…Recently, many efforts have been made and many works have been done, by proposing several advanced techniques or by improving some existing results in the literature in order to study or to reduce the conservatism of different classes of switched systems. Either continuous case or discrete‐time case, are considered for whether switched linear systems without delay (SLs), for example, in References 18‐21, or switched linear systems with constant delay (SLTDs); see, for example, References 22‐28 or with time‐varying delay (SLTVDs); see References 4,7,9,23,29‐39. Specifically, stability and stabilization of such systems are studied.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic stability and stabilization of discrete‐time switched systems with time‐varying delay

Charqi

Tissir

Boukili

2020

Optim Control Appl Methods

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Summary This article deals with the problems of stability and stabilization for a class of discrete‐time switched systems with time‐varying delay under arbitrary switching signal. First, sufficient conditions guaranteeing the asymptotic stability of the unforced system are developed, by using the switched Lyapunov‐Krasovskii functional method. Then, based on the obtained results, a state feedback controller is designed in order to ensure the asymptotic stability of the closed‐loop system. Furthermore, slack variables are introduced for more relaxation. The proposed approach is proved to have some less conservative results than some existing works. Finally, numerical examples are provided to illustrate the effectiveness and the merit of the proposed method and to compare the obtained results with some previous works in the literature.

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Stochastic Stability of Discrete-Time Switched Systems with a Random Switching Signal

Cited by 4 publications

References 13 publications

Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

A class of switched linear systems with persistent sojourn‐time expectation: Analysis and synthesis

Asymptotic stability and stabilization of discrete‐time switched systems with time‐varying delay

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