Guaranteed cost control of switched systems with neutral delay via dynamic output feedback

Abstract

This article is concerned with the problem of cost-guaranteed dynamic output feedback (DOF) control for a class of continuous-time linear switched system with both discrete and neutral delays. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed, in terms of a set of linear matrix inequalities (LMIs), to guarantee the exponential stability and a certain bound for the cost function of the closed-loop system, where the decay estimate is explicitly given to quantify the convergence rate. Then, the corresponding solvability conditions for a desired DOF controller under guaranteed cost are established by using the approach of linearising variable transforms. Since these obtained conditions are not all expressed by strict LMIs, the cone complementary linearisation method is exploited to cast them into sequential minimisation problems subject to LMI constraints, which can be easily solved numerically. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

Keywords:

• dynamic output feedback (DOF)
• exponential stability
• guaranteed cost control
• neutral delay
• switched systems

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 60804002, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Nuffield Foundation of the U.K. under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany.