PROBABILITY-GUARANTEED ROBUST FULL-ORDER AND REDUCED-ORDER H_∞-FILTERING

This paper addresses a robust H_∞ Linear Time-Invariant (LTI) filter synthesis problem for an affinely parameter-dependent LTI system, under the requirement that the filtering performance attained over the uncertainty polytope is guaranteed to a prescribed probability. The solution is based on a novel filtering-type Linear Matrix Inequality (LMI) formulation of the Bounded-Real Lemma (BRL) that guarantees an upper bound on the disturbance effect on the estimation error. The approach applies parameter-dependent Lyapunov functions and provides general full-order stationary filtering estimates; filters of reduced order are also obtained. The core of the probability aspect is a search for a truncated parameters- polytope which provides both the required probability and the best robust filtering performance level. The search for an appropriate truncated parameter-box - that has already been used for probabilistic performance analysis, state-feedback control synthesis, and structured disturbances modeling - leads to Bi-Linear Matrix Inequalities (BLMIs) which are solved by (convex) iterations. The probability requirement is expressed as a set of simple LMIs by recursively using a reduction lemma; these LMIs are concurrently solved with the above BLMIs. The features of the proposed probability-guaranteed robust filtering approach are demonstrated via an example.