On dwell time minimization for switched delay systems: Free-weighting matrices method

In this paper, we present a quasi-convex minimization method to calculate an upper bound of dwell-time for stability of switched delay systems. Piecewise Lyapunov-Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals are estimated by free weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for 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 (LMIs), dwell time optimization problem can be formulated as a standard quasi-convex optimization problem. Numerical examples are given to illustrate improvements over previously obtained dwell-time bounds.