Dwell time-based stabilisation of switched delay systems using free-weighting matrices - Koru, Ahmet Taha; Delibasi, Akin; Ozbay, Hitay (TAYLOR & FRANCIS LTD, 2018)
In this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov-Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities, dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.
Keywords: Time-delay; dwell time optimisation; switched delay systems; free-weighting matrices; LINEAR-SYSTEMS; STABILITY; OPTIMIZATION; FEEDBACK; Automation & Control Systems