Observer Design for Discrete-Time Nonlinear Systems Using the Stability Radii Theory

Abstract

This brief proposes an approach for designing state observers for a class of discrete-time nonlinear systems. This brief involves the concepts of positivity and stability radii. The approach consists of applying the stability radii technique of discrete-time positive systems with time-varying nonlinear functions in the estimation error dynamics to guarantee the exponential convergence property of the observer. The design conditions, only valid for Lipschitz-type nonlinearities, can be transformed in some situations into Linear Matrix Inequalities (LMIs). A numerical example is included to illustrate the effectiveness of the theoretical results.