H<inf>∞</inf> observer design for uncertain discrete-time nonlinear delay systems: LMI optimization approach

Abstract

In this paper, we present a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> observer for a class of nonlinear and uncertain time-delayed systems. To design the proposed observer, the time delay does not have to be exactly known. With knowledge about upper and lower bound of the delay term, we can design an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> observer that guarantees asymptotic stability of the estimation error dynamics and is robust against time-varying parametric uncertainties. We show that the described problem can be solved in terms of linear matrix inequalities (LMIs). In addition, the admissible Lipschitz constant of the system is maximized and the disturbance attenuation level is minimized through convex multi-objective optimization. Finally, the proposed observer is illustrated with an example.