Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems

This paper concerns the problems of stability and stabilization of a class of continuous-time linear switched systems with time-varying delays in the state. A delay-dependent stability criterion is formulated in terms of a set of linear matrix inequalities by constructing a piecewise quadratic Lyapunov function (PWQLF). Based on the stability result, the stabilization condition is obtained, and an algorithm involving convex optimization is adopted to find a set of memoryless state-feedback controllers such that system can be stabilized under a suboptimal maximal delay solved by the algorithm.