${\cal{H}}_{\infty}$ and ${\cal{L}}_{\bf 2}/{\cal{L}}_{\infty}$Model Reduction for System Input with Sector Nonlinearities

Abstract

This paper investigates the problems of model reduction for linear continuous-time systems with input sector nonlinearities. Two objectives (${\cal{H}}_{\infty}$ and ${\cal{L}}_{\bf 2}/{\cal{L}}_{\infty}$) 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.