This paper studies the dissipative filtering of uncertain singular time-varying delay Markovian jump systems (MJSs) with nonlinear perturbations and generally uncertain transition rates (GUTRs). We focus on the design of a mixed filter, which can include mode-dependent and mode-independent filters in a unified and simple structure. First, a new Lyapunov–Krasovskii functional is proposed through the delay-decomposition approach, and improved Wirtinger-based integral inequalities are used to obtain a sufficient condition to ensure the stochastic admissibility of the considered uncertain nonlinear singular time-varying delay MJSs with dissipative performance. Based on these ingredients, the explicit expression of the desired mixed filter is obtained. Finally, some numerical examples and the filter design of a two-loop circuit network reflect the less conservatism and effectiveness of the method in this article.
This paper addresses the observer-based control design for uncertain one-sided Lipschitz Markovian jump-delayed systems. By constructing the Lyapunov functional of the closed-loop augmented system, combining with the one-sided Lipschitz condition and quadratically inner-bounded condition, it is derived that the closed-loop augmented system is stochastic stable with an [Formula: see text] performance level [Formula: see text]. With the help of some special derivations, bilinear matrix inequalities are successfully transformed into a group of linear matrix inequalities. The robust controller and observer gains are solved by linear matrix inequality (LMI) toolbox in MATLAB.
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