Mixed L/sub 2/-L/spl infin//H/spl infin/ filtering for uncertain linear systems: An LMI approach

摘要

The problem of full-order mixed L/sub 2/-L/spl infin//H/spl infin/ performance filtering design for uncertain linear systems is addressed in this paper. The uncertain parameters are assumed to belong to convex bounded domains (i.e., polytope type uncertainty). The main purpose is to design a stable linear filter such that the filtering error output signal remains bounded, using a mixed L/sub 2/-L/spl infin//H/spl infin/ performance index as criterion. In the mixed L/sub 2/-L/spl infin//H/spl infin/ filtering design, an upper bound to the peak value of the filtering error over all the energy bounded noise signals is minimized while an H/spl infin/ constraint is assured. The conditions for the existence of such a robust filter are provided in terms of linear matrix inequalities-LMIs, allowing the use of standard convex optimization procedures to solve the problem. Both continuous- and discrete-time systems are considered. The formulation presented is illustrated by one example.