Chapter 18 - Observer-based stabilization of nonlinear discrete-time systems using sliding window of delayed measurements

Abstract

In this chapter, a relevant H∞ observer-based stabilization design methodology for Lipschitz nonlinear discrete-time systems is proposed. The objective is to develop a novel H∞ observer-based controller so that wider ranges of problems can be solved without too much of mathematics overhead. This new method is based on adding delayed measurements to the Luenberger observer and delayed states to the feedback controller which provide nonrestrictive sufficient conditions. The established sufficient stability conditions are in the form of bilinear matrix inequality (BMI) transformed, through a useful approach, to a convex problem (linear matrix inequality-LMI). A comparison with the classical approach (that uses standard forms of the Luenberger observer and the feedback controller) is presented. This comparison shows that the proposed observer-based controller is less restrictive and offers greater degree of freedom. Two numerical examples are implemented to validate high performances of the proposed approach.