New results on H∞ filtering for Markov jump systems with uncertain transition rates

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In this paper, we study the H∞ filtering problem for a class of continuous-time Markov jump systems with time-varying uncertainties in transition rates, in which the uncertain transition rates are assumed to be affine parameter-dependent uncertainty models. By converting the affine parameter-dependent uncertainty models for transition rates into time-varying polytopic ones and using the Lyapunov function approach, a sufficient condition on the existence of an H∞ filter is obtained in terms of a parameter-dependent matrix inequality. Also, the parameter-dependent matrix inequality is converted into a set of parameter-free linear matrix inequalities which can be solved numerically. Illustrative examples are given to demonstrate the effectiveness and advantages of the approach.