Disturbance Attenuation in Classes of Uncertain Linear Hybrid Systems

Hai Lin and Panos J.Antsaklis

Proceedings of the 2004 American Control Conference, pp.566-571, Boston, MA, June 30- July 2, 2004

Abstract—In this paper, we study the disturbance attenuation properties for some classes of discrete-time uncertain piecewise linear hybrid/switched systems, which are affected by both time-variant parameter variations and persistent exterior disturbances. The problem of determining nonconservative bounds on the l1 induced gain from the disturbance to controlled output for the closed-loop uncertain linear hybrid system is investigated. A procedure is given to determine such minimal l1 norm of the uncertain piecewise linear systems. However, the termination of the procedure developed for general uncertain piecewise linear systems is not guaranteed. Therefore, it is important to specify a subclass of piecewise linear systems whose l1 norm can be determined in finite number of steps. For such a purpose, we simplify the discrete event dynamics of the uncertain hybrid systems and obtain its subclass called uncertain switched linear systems. It is shown that the uncertain switched linear systems’ l1 norm can be determined in finite number of steps.

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