Abstract: The problem of stability analysis and control for consisting of a class of multiple subsystem of switched systems with time-delay are studied,sufficient conditions of switched system asymptotic stability are given be using linear matrix inequality.Condition of asymptotic stability of the switched systems and design technique of the switch laws by using multiple lyapunov function were given.Design technique  based on multiple Lyapunov Function can be expressed as linear matrix inequalities.The corresponding linear matrix inequalities based algorithms for determining stability bounds were derived.The switch laws and the maximum perturbation to ensure system stability can be calculated.The switched system consisting of multiple subsystems is simulated.The simulation results show effectiveness of the methods.

Key words: switched system with time-delay, stability analysis and control, linear matrix inequality, stability bounds