Output feedback control of switched systems: Instrumental matrix method

A new and simple approach to design output feedback controllers for switched systems is proposed in this paper. The bilinear inequality including Lyapunov matrix and output feedback gain matrix is decoupled by introducing additional instrumental matrix variable. Combined with multiple Lyapunov function method, the bilinear inequality is transformed into linear matrix inequality (LMI). The sufficient conditions of, under designed switching signal, asymptotical stability of closed-loop switched system via static and dynamic output feedback are presented, respectively. The proposed conditions do not require the decomposition of Lyapunov matrix and its inverse matrix and fix the structure of Lyapunov matrix. The theoretical results are verified by means of an example.