Quadratic Stability of Linear Time-Delayed Switched Systems with Polytopic Perturbations

The problem of quadratic stability of linear time-delayed switched systems with polytopic perturbations is considered. The perturbation is formed by a polytopic which is spanned by a number of constant known matrixes. By using condition of completeness, Lyapunov asymptotic stability theory and linear matrix inequality (LMI) method, delay independent quadratic stability conditions and the switching law of the uncertain delayed switched system are derived. Then by defining linear transformation, the delayed system can be converted to a delay-free system, and consequently delay dependent quadratic stability conditions and the switching law of the uncertain delayed switched system are obtained. The simulation results show the validity of the switching law