Robust Exponential Stability for Uncertain Discrete-Time Switched Systems with Interval Time-Varying Delay through a Switching Signal

 

Jenq-Der Chen¹*, I-Te Wu², Chang-Hua Lien³, Chin-Tan Lee⁴, Ruey-Shin Chen⁵ and Ker-Wei Yu⁶

 

^1,5 Department of Computer Science and Information Engineering. National Quemoy University, Kinmen, Taiwan, R.O.C. *tdchen@nqu.edu.tw.

² Department of Life Science-National Taiwan Normal University and Department of Sports and Leisure National Quemoy University Kinmen, Taiwan , R.O.C.

^3,6 Department of Marine Engineering, National Kaohsiung Marine University Kaohsiung, Taiwan , R.O.C.

⁴ Department of Electronic Engineering, National Quemoy University, Kinmen, Taiwan , R.O.C.

 

Abstract

This paper deals with the switching signal design to robust exponential stability for uncertain discrete-time switched systems with interval time-varying delay. The lower and upper bounds of the time-varying delay are assumed to be known. By construction of a new Lyapunov-Krasovskii functional and employing linear matrix inequality, some novel sufficient conditions are proposed to guarantee the global exponential stability for such system with parametric perturbations by using a switching signal. In addition, some nonnegative inequalities are used to provide additional degrees of freedom and reduce the conservativeness of systems. Finally, some numerical examples are given to illustrate performance of the proposed design methods.

Keywords: Switching signal, exponential stability, discrete switched systems, interval time-varying delay, additional nonnegative inequality.

 

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Acknowledgments

The research reported here was supported by the National Science Council of Taiwan, R.O.C. under grant no. NSC102-2221-E-507-006.

 

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