A Linear Matrix Inequality Approach to The Peak-to-Peak Guaranteed Cost Filtering Design

Abstract The problem of robust filtering design for uncertain linear systems with guaranteed peak-to-peak performance is addressed in this paper. The uncertain parameters are assumed to belong to convex bounded domains (i.e. polytope type uncertainty). The aim is to design a full-order stable linear filter that minimizes the worst-case peak value of the filtering error output signal with respect to all magnitude bounded noise inputs, in such way that the filtering error system remains robustly stable. The minimization provides an upper bound to the L ∞ induced gain ( l ∞ for discrete-time systems) of the filtering error system. The conditions for the existence of such robust filter are provided in terms of linear matrix inequalities, allowing the use of standard convex optimization procedures to solve the problem. Both continuousand discrete-time systems are considered. The formulation presented is illustrated by examples.

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