H∞ filter design for discrete-time linear systems with sector-bounded nonlinearities: an LMI approach

This paper concerns the problem of full-order and reduced-order H_∞ filter design for discrete-time system with sector-bounded nonlinearities. The purpose of this paper is to design full-order and reduced-order filter with the same nonlinearity such that the filtering error system is asymptotically stable and has a guaranteed H_∞ performance. By using slack variable technique, sufficient conditions are obtained for the existence of admissible filters. Moreover, in order to overcome the non-convex constraint for reduced-order H_∞ filter design, by converting the structural constraint on the Lyapunov matrix to the constraint on the slack variables, the admissible filter can be obtained from the solution of convex optimization problem in terms of linear matrix inequality, which can be solved via efficient interior-point algorithms. Numerical example is presented to illustrate the effectiveness of the proposed methods.