Stabilisation for switched linear systems with time-varying delay and input saturation

Abstract

This article investigates the stabilisation problems for continuous-time and discrete-time switched systems with time-varying delay and saturated control input. Based on dwell time switching signals and multiple Lyapunov functional method, stabilisation conditions are well obtained in the context of linear matrix inequalities. To estimate attractive regions as large as possible, the feasibility problems are translated into optimisation problems. In addition, the corresponding results are presented for linear time-delay systems and switched delay-free systems, which improve and supplement some existing ones in the literature. Finally, numerical examples and simulations are given to illustrate the effectiveness and values of the proposed results.

Keywords:

• stabilisation
• switched linear systems
• time-varying delay
• input saturation

Acknowledgements

This work was partly supported by National Natural Science Foundations of P.R. China under Grants 61273119, 61004046, 61174076 and 61104068 and was also partly supported by the Research Foundations for the Doctoral Program of Higher Education of PR China under Grants 20090092120027 and 20110092110021.