Explicit Hybrid Optimal Controller for Disturbance Attenuation in Linear Hybrid Systems

Hai Lin, Guisheng Zhai, and Panos J. Antsaklis

Proceedings of the 16th IFAC World Congress
Prague, Czech Republic, July 4-8, 2005.

Abstract—In this paper, the disturbance attenuation properties for classes of linear hybrid systems perturbed by exterior disturbances are investigated, and a hybrid l_inf robust optimal control problem is studied. First, a procedure is developed to determine the minimal l_inf induced gain of linear hybrid systems. However, for general hybrid systems, the termination of the procedure is not guaranteed. Then, the decidability issues are briefly discussed. Finally, we study the robust l_inf optimal controller synthesis problem. It is shown that the optimal performance level can be achieved by a piecewise linear state feedback control law for the linear hybrid systems, and a systematic approach to design such feedback control is proposed.

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