Overcoming non‐convexity of the robust nonlinear output feedback problem: An adaptive linear matrix inequality solution

Abstract

AbstractThis article presents a novel solution for adaptive output feedback of uncertain nonlinear systems; it uses nonlinear controller and observer structures to drive a time‐varying function as a Lyapunov one, thus guaranteeing asymptotic stability of the system states and observation error. Exact convex modeling of available terms and polytopic embedding of unavailable ones in the Lyapunov function dynamics, allow linear matrix inequalities to be used, thus overcoming former difficulties over the non‐convex nature of the problem. Moreover, the proposal incorporates a recently appeared factorization to get rid of approximate solutions based on Lipschitz bounds and persistence of excitation. The methodology is successfully put at test against related works in a variety of examples.