Input-to-state stability and optimal control of a class of switched systems

A new approach to solve input-to-state stability (ISS) and optimal control problems of a class of switched systems is presented based on the average dwell time approach in the paper. A new form of objective function is constructed such that switched system is input-to-state stability. Compared with existing approaches, conditions that constructing ISS control Lyapunov function and (or) all ISS subsystems are not needed. It's great convenient that optimal design of subsystem's controller by using optimal control theory of continuous system. Constraint conditions of optimal control problem are transformed into linear constraints. Optimal results can be got by solving differential algebraic equations. Results of numerical simulation are provided to support the proposed method in the paper.