Disturbance attenuation in classes of uncertain linear hybrid systems

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 l/sup /spl infin// 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 l/sup 1/ 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 l/sup 1/ 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´ l/sup 1/ norm can be determined in finite number of steps.