Improved results on exponential stability of discrete-time switched delay systems

Xiang Xie; Honglei Xu; Xinming Cheng; Yilun Yu

doi:10.3934/dcdsb.2017010

Article Contents

2017, Volume 22, Issue 1: 199-208. Doi: 10.3934/dcdsb.2017010

This issue Previous Article Z-Eigenvalue Inclusion Theorems for Tensors Next Article pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations

Improved results on exponential stability of discrete-time switched delay systems

1.
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
2.
Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia
3.
School of Information Science and Engineering, Central South University, Changsha, Hunan 410083, China

* Corresponding author
* Corresponding author

Received: July 31, 2015

Revised: April 30, 2016

Published: November 2017

The work is supported by the National Natural Science Foundation of China (11171079) and the Australian Research Council (DP160102819)

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Abstract

In this paper, we study the exponential stability problem of discrete-time switched delay systems. Combining a multiple Lyapunov function method with a mode-dependent average dwell time technique, we develop novel sufficient conditions for exponential stability of the switched delay systems expressed by a set of numerically solvable linear matrix inequalities. Finally, numerical examples are presented to illustrate less conservativeness of the obtained results.

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Mathematics Subject Classification: Primary:58F15, 58F17;Secondary:53C35.

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Figure 1. State trajectories of switched system under ADT switching with $\tau _a = 2$

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Figure 2. State trajectories of switched system under MDADT switching with $\tau _{a1} = 1, \tau _{a2} = 1, \tau _{a3} = 1, \tau _{a4} = 2$

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Table 1. Computation Results For The Switched Delay System (9) Under Two Different Switching Schemes

Switching Schemes	ADT Switching	MDADT Switching
Criteria for controller design	Theorem 1 in [19]	Theorem 1 in this paper
Switching signals	$\tau _a^* = 0.1175$ $\mu = 1.1$ $\lambda \le 1.5$	$\tau _{a1}^* = 0.0312$, $\tau _{a2}^* = 0.0409$, $\tau _{a3}^* = 0.0642$, $\tau _{a4}^* = 0.1175$, ${\mu _1} = {\mu _2} = {\mu _3} = {\mu _4} = 1.1$, ${\lambda _1} \le 4.6$, ${\lambda _2} \le 3.2$, ${\lambda _3} \le 2.1$, ${\lambda _4} \le 1.5$

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