Abstract
This paper deals with the robustH∞filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribedH∞performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.
Highlights
Time delay exists extensively in chemical process systems, communication systems, economic systems, microwave oscillator, and networked control systems
The appearance of time delay and uncertainties in many systems can often bring instability, oscillation, and poor performance; considerable attention has been focused on the stability analysis of uncertain time delays systems; see [1,2,3,4,5,6] and the references therein
The stochastic effects can lead to oscillation, divergence, or other poor performances
Summary
Time delay exists extensively in chemical process systems, communication systems, economic systems, microwave oscillator, and networked control systems. Many methods are proposed in the process of robust stochastic stability analysis and filtering design, which develops from the early solving Riccati equation to model transformation method and cross-terms bounding technique [5], free-weighting matrices method [11, 32], slack matrix variables [17,18,19, 24, 28], and delay-partitioning method [20]. To the best of the authors’ knowledge, the H∞ filtering problem has not been reported about uncertain neutral stochastic systems with Markovian jumping parameters and time delay, which motivates the present study. Motivated by the works in [5, 13, 17, 18], the robust H∞ filtering for uncertain neutral stochastic systems with Markovian jumping parameters and time delay is considered in this paper. E{⋅} stands for the mathematical expectation operator with respect to the given probability measure P
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