Robust Control for a Class of Nonlinear Systems

Tlili saber¹, Mibar hassen²

Unit of research (RME), INSAT, Tunisia
Centre urbain Nord, B.P. N°676, 1080 Tunis Cedex, Tunisia

Abstract
This paper is concerned with the control problem synthesis for nonlinear systems using linear technique. The proposed algorithm consists on an approximation of the non-linear systems by a set of uncertain linear models and presents a systematic approach for non-linear control design by using the gain scheduling technique to insure the transition of a non-linear dynamical process from an actual operating condition to a desired one. The non-linear system is represented in neighborhood of equilibrium points by a family of uncertain linear systems. A robust control law is built so as to insure asymptotic stability to a given equilibrium within a maximal ellipsoidal region. Given a pre-specified equilibrium curve connecting the initial and final points. Output feedback for the local robust control synthesis are considered, together with local performance criteria. A simple numerical experiment is provided to illustrate both the effectiveness of the synthesis and the performance achieved.

Keywords: Robust control, Gain Scheduling, Transition Control, Norm bounded uncertainties, Linear Matrix Inequalities (LMI).

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