Delay-dependent Robust Stabilizability Criterion for Switched Time-delay Systems with Polytopic Uncertainties

This paper studies the robust stabilization problem for linear continuous-time systems with time-delay that are composed of polytopic uncertain subsystems. The approach followed in this note aims at the existence of common positive definite matrices for all convex combinations of the extreme points which belong to different subsystem matrices to check robust stability of the switched system. The stability condition of delay-dependent is analyzed by a new bounding method and is given in terms of bilinear matrix inequalities (BMI). Based on the obtained result, we also design the switching rule by the obtained common positive definite matrices.