Adaptive observer design for a class of nonlinear systems with time delays

Abstract

This paper deals with the design of adaptive observer for a class of nonlinear systems with time delays. Within this work, we develop an adaptive observer for a bilinear time delay system, then we extend those results in the presence of Lipschitz nonlinear functions in the system's dynamics. In the stability analysis of the estimation errors, we combine a Linear Parameter Varying (LPV) approach in the presence of time delays with a polytopic approach. The obtained stability conditions are given in terms of the solvability of Linear Matrix Inequalities (LMIs) on the vertices of a convex polytope. Numerical examples are finally given to show the effectiveness and feasibility of our results.