New results on the quadratic stabilization of switched linear systems

We consider the quadratic stabilization of switched linear systems when a switching strategy is added on the state feedback controllers or on the output feedback controllers of subsystems. Two sufficient conditions are established respectively to guarantee the quadratic stabilization for both cases. For state feedback case, these two sufficient conditions are also necessary when there are only two subsystems. In particular, for planar case, it is shown that the quadratic stabilization problem reduces to the verification of two linear independent input matrices and a method is given to design the concrete state feedback gain matrices. For output feedback case, a necessary condition on the quadratic stabilization problem is also given by the concept of fixed modes. For both cases, we propose the switching rules by using the obtained feedback gain matrices and an associated positive definite matrix.