Stabilization of linear systems with sector bounded nonlinearities at the input and output

In this paper we propose a general quadratic dissipativity output feedback control method to solve a robust stabilization problem for linear systems with sector bounded type nonlinearities at the input and out put. The problem includes the one of achieving specified gain and phase stability margins as a special case. We pose the problem as one of finding a controller for a new, related linear system such that the closed loop system is dissipative with respect to a specifically chosen quadratic supply rate. We employ the information method to derive the desired controller. Stability results are obtained using the Lyapunov methods. We provide an example to demonstrate the utility of the proposed control method.