Stability and stabilisation of switched time-varying delay systems: amultiple discontinuous Lyapunov function approach

Iman Zamani | Mohammad Mahdi Saberi

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=137767
Date :  2020/07/18
Publish in :    International Journal of Systems Science

Link :  https://www.tandfonline.com/doi/abs/10.1080/00207721.2020.1794081
Keywords :Switched systems; time-varying delay; multiple discontinuous Lyapunov function (MDLF) sliding mode control; mode dependent average dwell time (MDADT)

Abstract :

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In this paper, stability and stabilisation of switched time-varying delay systems are investigated. By developing, a multiple discontinuous Lyapunov function approach and using the mode-dependent average dwell time (MDADT) switching signal, sufficient conditions are first proposed to guarantee the exponential stability of the switched system with stable and unstable subsystems where the time-varying delay is considered in the states. Relaxed stability conditions are also obtained by using a form of the Bessel–Legendre inequality. Then stabilisation of the proposed system is presented by designing a sliding mode controller. Sufficient conditions and sufficient relaxed conditions of a reduced-order sliding mode dynamics are derived, and desired sliding surfaces in the form of linear matrix inequalities (LMIs) are also given. The obtained conditions are checked by using the combined genetic algorithm and convex programming techniques. Moreover, some numerical and practical examples are given to illustrate the effectiveness of the obtained theoretical results.