H∞ and L2/L∞ model reduction for system input with sector nonlinearities

This paper investigates the problems of model reduction for linear continuous-time systems with input sector nonlinearities. Two objectives ( H-infinity and L-2/L-infinity) are employed to evaluate the approximation performance and the problems are solved by using linear matrix inequality (LMI) techniques, with sufficient conditions obtained for the existence of desired reduced-order models. Since some matrix inequality constraints are involved in these conditions, the cone complementarity linearization idea is utilized to cast the nonconvex feasibility problem into a sequential minimization problem subject to LMI constraints. A numerical example is presented to show the effectiveness of the proposed theories.