Guaranteed cost nonlinear sampled-data control: applications to a class of chaotic systems

Abstract

This paper addresses the guaranteed cost sampled-data controller synthesis and analysis problems with application to nonlinear chaotic systems. A linear parameter-varying (LPV) model is utilized to represent the nonlinear behaviour of the chaotic system while the gap between the measured and real parameters of the controller and plant are considered as bounded uncertainties. Using the LPV model coupled with the uncertainties, a modified parameter-dependent Lyapunov functional method is utilized and a sampled-data controller is developed that locally asymptotically stabilizes the nonlinear system with guaranteed predefined cost function upper bound. Moreover, employing the cost function upper bound minimization, a suboptimal sampled-data LPV controller is proposed. The central contribution of this work is to present a novel LMI-based formulation with the less conservative results, and thereby, an LMI-based LPV suboptimal sampled-data controller synthesis procedure is developed for nonlinear chaotic systems. The proposed procedure is readily solved by the aid of available off-the-shelf convex optimization techniques. Finally, the proposed sampled-data LPV controller is applied to the well-known chaotic Lorenz and Rossler systems, and the results verify the effectiveness and less conservativeness of the proposed method compared to some state-of-the-art techniques.