A Lie Algebraic Condition of Stability for Hybrid Systems and Application to Hybrid Synchronization

Zhao, Shouwei

doi:10.1142/s0218127409022932

Cited by 7 publications

(7 citation statements)

References 17 publications

(22 reference statements)

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“…Moreover, it can be seen that (34) ensures (8). Hence, according to Lemma 1, we have system (18)- (19) is GUAS.…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 75%

“…Hence, switched linear system (18)- (19) is GUAS and has a l 2 -gain performance index under any MDADT switching signal satisfies…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 99%

“…Therefore, according to Definition 3 for any switching signals satisfying p > * p = − ln ln(1 − ) switched system (18)- (19) is GUAS and has a l 2 -gain performance index .…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 99%

“…In the following Theorem, a feasible QTD H ∞ controller is designed such that system (18)- (19) is GUAS. Theorem 3.…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 99%

“…Theorem 3. Consider discrete-time switched linear system (18)- (19). Let > 0, 0 < < 1, and > 1 be given constants, if there exists a set of symmetric positively definite matrixes P i (q), q = 0, 1 · · · p , ∀i ∈  such that…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 99%

See 4 more Smart Citations

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

Zheng

Sun

Ren

et al. 2017

Asian Journal of Control

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This paper is concerned with the stability and stabilization problem of a class of discrete-time switched systems with mode-dependent average dwell time (MDADT). A novel Lyapunov function, which is both mode-dependent (MD) and quasi-time-dependent (QTD), is established. The new established Lyapunov function is allowed to increase at some certain time instants. A QTD H ∞ controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed H ∞ performance index. The new QTD robust controller designed in this paper is less conservative than the mode independent one which is frequently considered in literatures. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the developed results.Definition 2. For a switching signal (t) and any T ≥ t ≥ 0, let N p (T, t) be the switching numbers and the p th subsystem is activated over the interval [t, T]. T p (T, t) denotes the total running time of the p th subsystem over the interval [t, T] with p ∈ . We say that (t) has a mode-dependent average dwell time p if there exists a positive number N 0p (We call N 0p the mode-dependent chatter bounds here) and p satisfyDefinition 3 ([26]). For > 0, system (1)-(2) is said to be GUAS with an l 2 -gain, if under zero initial condition, system (1)-(2) is GUAS and ‖z‖ l 2 [0,T] ≤ ‖ ‖ l 2 [0,T] holds for all nonzero ∈ l 2 [0, T], 0 ≤ T < ∞.Definition 4. For > 0 and let 0 < < 1, the switched system (1)-(2) is said to be GUAS with an l 2 -gain, if under zero initial condition, system (1)-(2) is GUAS and ∑ ∞ k=k 0(1 − )z T (k)z(k) ≤ ∑ ∞ k=k 0

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“…Moreover, it can be seen that (34) ensures (8). Hence, according to Lemma 1, we have system (18)- (19) is GUAS.…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 75%

“…Hence, switched linear system (18)- (19) is GUAS and has a l 2 -gain performance index under any MDADT switching signal satisfies…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 99%

“…Therefore, according to Definition 3 for any switching signals satisfying p > * p = − ln ln(1 − ) switched system (18)- (19) is GUAS and has a l 2 -gain performance index .…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 99%

“…In the following Theorem, a feasible QTD H ∞ controller is designed such that system (18)- (19) is GUAS. Theorem 3.…”

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 99%

Section: L 2 -Gain Performance Analysis and Qtd H ∞ Controller Dementioning

confidence: 99%

See 3 more Smart Citations

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

Zheng

Sun

Ren

et al. 2017

Asian Journal of Control

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A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization

Zhao

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.

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A New Fuzzy Impulsive Control of Chaotic Systems Based on T–S Fuzzy Model

Liu

Zhao

2011

IEEE Trans. Fuzzy Syst.

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A Lie Algebraic Condition of Stability for Hybrid Systems and Application to Hybrid Synchronization

Cited by 7 publications

References 17 publications

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization

A New Fuzzy Impulsive Control of Chaotic Systems Based on T–S Fuzzy Model

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