Input-to-State Stability of Time-Varying Switched Systems With Time Delays

Wu, Xiaotai; Tang, Yang; Cao, Jinde

doi:10.1109/tac.2018.2867158

Cited by 107 publications

(51 citation statements)

References 28 publications

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“…Remark In the work of Xiang and Xiao, switched systems with all modes unstable can be stabilized by switching behavior, that is, the switching behavior can also be seen as a good factor instead of only a bad factor that destroying stability. Therefore, compared with the work of Wu et al (where μ i >1) and the work of Ren and Xiong, in our paper, μ i >0 (in condition (iii) of Theorem ) means that switching behavior between subsystems could be stabilizing or destabilizing. Similarly, if

d_{j} > 1, j \in ℐ

, the j th impulsive jump map could be seen as destabilizing impulsive effect, in turn, if 0< d j <1, then the j th impulsive jump map could be seen as stabilizing impulsive effect.…”

Section: Resultsmentioning

confidence: 57%

“…Condition (vi) implies that the switching and impulsive effects should act frequently. Compared with the stability results in the work of Wu et al, where there must exist at least one stable subsystem, Theorem allows for all unstable modes in switched system . Theorem implies that the switched system can be stabilized under switching and impulsive effects.…”

Section: Resultsmentioning

confidence: 96%

“…Therefore, both stabilizing and destabilizing switches and impulses can coexist in the considered systems, condition (v) provides a design method to balance the switching and impulsive effect for guaranteeing the stability of system . When there is no impulsive effect and μ i >1,∀ i ∈ S , then

S_{1} = \emptyset {, ℐ}_{1} = \emptyset, frakturp = 1

, Theorem reduces to theorem 1 in the work of Wu et al…”

Section: Resultsmentioning

confidence: 99%

“…Example Consider the consensus of two nonlinear agents as in the work of Wu et al with impulsive effect

({, \begin{matrix} array {\dot{x}}_{l} (t) = f_{σ (t)} (x_{l} (t - τ (t))) + ω_{l} (t) + u_{l} (t), t \geq 0, t \notin T_{1} ⋃ T_{2}, \\ array x_{l} (t) = \{\begin{matrix} 0.63 x_{l} false(t^{-} false), & t \in T_{1} = false{1, 3, 5, … false}, \\ 1.3 x_{l} false(t^{-} false), & t \in T_{2} = false{2, 4, 6, … false}, \end{matrix} \\ array x_{1} (s) = 4, s \in [- 0.1, 0], \\ array x_{2} (s) = - 4, s \in [- 0.1, 0], \end{matrix})

where

f_{1} false(x_{l} false(t - τ false(t false) false) false) = \sin false(x_{l} false(t - τ false(t false) false) false), f_{2} false(x_{l} ...

…”

Section: Simulation Examplesmentioning

confidence: 99%

“…Time delay is a common phenomenon in practical systems, which causes the evolution of a system's state depends not only on the current status but also on the historical information. The existence of delay may lead to instability and poor performance; thus, it is necessary to consider time delay in the stability analysis …”

Section: Introductionmentioning

confidence: 99%

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Input/output‐to‐state stability of impulsive switched delay systems

Hong

Zhang

2019

Intl J Robust & Nonlinear

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Summary This paper investigates the input/output‐to‐state stability (IOSS) and integral IOSS (iIOSS) of nonlinear impulsive switched delay systems where the switching moments and impulsive moments do not necessarily coincide with each other. Some Razumikhin‐type criteria are presented to guarantee the IOSS and iIOSS of the systems, where both destabilizing and stabilizing effects of switching behavior and impulses are considered simultaneously. The counterpart results for impulsive switched systems without delay can be naturally obtained. Several examples are provided to verify the effectiveness and superiority of the proposed results.

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d_{j} > 1, j \in ℐ

, the j th impulsive jump map could be seen as destabilizing impulsive effect, in turn, if 0< d j <1, then the j th impulsive jump map could be seen as stabilizing impulsive effect.…”

Section: Resultsmentioning

confidence: 57%

Section: Resultsmentioning

confidence: 96%

S_{1} = \emptyset {, ℐ}_{1} = \emptyset, frakturp = 1

, Theorem reduces to theorem 1 in the work of Wu et al…”

Section: Resultsmentioning

confidence: 99%

“…Example Consider the consensus of two nonlinear agents as in the work of Wu et al with impulsive effect

({, \begin{matrix} array {\dot{x}}_{l} (t) = f_{σ (t)} (x_{l} (t - τ (t))) + ω_{l} (t) + u_{l} (t), t \geq 0, t \notin T_{1} ⋃ T_{2}, \\ array x_{l} (t) = \{\begin{matrix} 0.63 x_{l} false(t^{-} false), & t \in T_{1} = false{1, 3, 5, … false}, \\ 1.3 x_{l} false(t^{-} false), & t \in T_{2} = false{2, 4, 6, … false}, \end{matrix} \\ array x_{1} (s) = 4, s \in [- 0.1, 0], \\ array x_{2} (s) = - 4, s \in [- 0.1, 0], \end{matrix})

where

f_{1} false(x_{l} false(t - τ false(t false) false) false) = \sin false(x_{l} false(t - τ false(t false) false) false), f_{2} false(x_{l} ...

…”

Section: Simulation Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Input/output‐to‐state stability of impulsive switched delay systems

Hong

Zhang

2019

Intl J Robust & Nonlinear

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Finite‐time asynchronous control of linear time‐varying switched systems

Wang

Xing

Xiang

2021

Adaptive Control & Signal

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In the framework of asynchronous control, finite-time stabilization and finite-time bounded stabilization of linear time-varying (LTV) switched systems are investigated. A necessary and sufficient condition for finite-time stability (FTS) of LTV switched systems is proposed based on differential matrix inequalities (DMIs). Moreover, we extend the FTS result to the case of finite-time boundedness (FTB), and present a sufficient condition of FTB for LTV switched systems using the average dwell time method which can be used for design proposes. Then we turn to the design problem of asynchronously switched control to guarantee FTS or FTB of LTV switched systems and give a sufficient condition for the state feedback stabilization in the form of nonlinear DMIs (NDMIs). A numerical method is proposed to solve NDMIs approximately. Finally, two examples are given to illustrate the validity of the results.

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Input‐to‐state stability for discrete‐time time‐varying impulsive switched delayed systems with asynchronous phenomena

Peng

2022

Asian Journal of Control

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This paper studies the input-to-state stability (ISS) for a class of discrete-time time-varying impulsive switched delayed systems, in which the asynchronous phenomena are considered. Asynchronous phenomena here include two implications: asynchronous impulses and switches and asynchronous switching. The former means that the events, that is, impulses and switches, are not necessary to occur simultaneously, while the latter indicates that the actual switching modes and related controllers or specified modes do not coincide. Applying the mode-dependent concept to impulses and switches, both the improved Krasovskii-type and Razumikhin-type ISS criteria are provided. The time differences of Lyapunov functionals or functions here are sign-changing and time-varying, releasing from the traditional assumption that always requires negative definiteness. Meanwhile, in this paper, ISS or non-ISS subsystems and stabilizing or destabilizing impulses are taken into account. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.

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Input-to-State Stability of Time-Varying Switched Systems With Time Delays

Cited by 107 publications

References 28 publications

Input/output‐to‐state stability of impulsive switched delay systems

Input/output‐to‐state stability of impulsive switched delay systems

Finite‐time asynchronous control of linear time‐varying switched systems

Input‐to‐state stability for discrete‐time time‐varying impulsive switched delayed systems with asynchronous phenomena

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