Extended Dissipative Filtering for Markovian Jump Interval-Valued Fuzzy Systems with Uncertain Transition Rates.

This paper addresses the problem of the extended dissipative filtering for a class of Markovian jump interval-valued fuzzy systems with uncertain transition rates. First, a sufficient condition of stochastic asymptotic stability and extended dissipativity is provided. Then, by introducing some additional matrices, the matrices in this sufficient condition can be decomposed into a form with only one part and its transpose containing the unknown parametric matrices of filter, which is vitally important for establishing a new sufficient condition and designing an extended dissipative filter via the Projection Lemma. Attention is focused on the applications of this Projection Lemma twice by virtue of the feature of extended dissipative performance which differs from existing work and produces better estimated effects. The new sufficient condition is of nonlinear form with respect to some matrix variables, which makes the determination of extended dissipative filter difficult. Fortunately, by transforming nonlinear matrix inequalities into a quadratic optimization problem with linear matrix inequality constraints, the extended dissipative filter is developed by virtue of a cone complementarity linearization algorithm. Finally, two numerical examples are given to show the effectiveness of our proposed approach.