Stability Analysis of a Class of Switched Time-delay Systems with Unstable Subsystems

This paper analyzes the stability of a class of linear switched time-delay systems which contain unstable subsystems. Stability conditions are derived by applying the descriptor transformation and developing a new technique in the derivative of the Lyapunov functional, such that the effects of the mixed states are included. Consequently, the resulting delay dependent stability criteria are less conservative compared to the published work in the literature. It is also shown that not only the stability of the system but also the region of the ultimate boundedness are dependent on the size of the delay.