Quantized ℋ∞ Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information

This paper investigates the problem of quantized ℋ∞ filtering for a class of continuous‐time Markovian jump linear systems with deficient mode information. The measurement output of the plant is quantized by a mode‐dependent logarithmic quantizer, and the deficient mode information in the Markov stochastic process simultaneously considers the exactly known, partially unknown, and uncertain transition rates. By fully exploiting the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for quantized ℋ∞ performance analysis is first derived, and then two approaches, namely, the convex linearization approach and iterative approach, to the ℋ∞ filter synthesis are developed. It is shown that both the full‐order and reduced‐order filters can be obtained by solving a set of linear matrix inequalities (LMIs) or bilinear matrix inequalities (BMIs). Finally, two illustrative examples are given to show the effectiveness and less conservatism of the proposed design methods.