Optimal Persistent Disturbance Attenuation Control for Linear Hybrid Systems

Hai Lin, Guisheng Zhai, Panos J. Antsaklis

Nonlinear Analysis Theory, Methods and Applications-Special Issue: Hybrid Systems and Applications
Vol.65, No.6, pp 1231-1250, September 2006.

Abstract—In this paper, the disturbance attenuation properties for a class of linear hybrid systems are investigated, and a hybrid optimal persistent disturbance attenuation control problem is studied. First, a procedure is developed to determine the minimal l∞ induced gain of linear hybrid systems. However, for general hybrid systems, the termination of the procedure is not guaranteed. Then, the decidability issues are discussed. The termination of the procedure in nite number of steps is shown for a subclass of hybrid systems with simplied discrete event dynamics, called switched linear systems. Finally, the optimal persistent disturbance attenuation controller synthesis problem is studied. It is shown that the optimal performance level can be achieved by a piecewise linear state feedback control law, and a systematic approach is proposed to design such feedback control.

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