Search

This paper is devoted to the investigation of the delay-dependent filtering problem for a class of continuous-time singular Markov jump systems with Wiener process and generally uncertain transition rates (GUTRs). In the GUTR stochastic singular model under consideration, based on an auxiliary vector function, by employing an integral inequality and some appropriate free-weighting matrices, the delay-dependent sufficient conditions are derived, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, impulse-free and stochastically stable, but also satisfies a prescribed performance for all time-varying delays no larger than a given upper bound. Furthermore, the solvability conditions of the filtering problem are deduced in terms of a new type of candidate Lyapunov-Krasovskii function and a set of matrix inequalities. Finally, simulation examples are performed to validate the proposed method in this paper. [ABSTRACT FROM AUTHOR]

The mean-square admissibility problem of stochastic T–S fuzzy singular systems via an extended quadratic Lyapunov function is investigated in this paper. Comparing with the existing quadratic Lyapunov function method, the extended quadratic Lyapunov function method can relax stabilization conditions. Firstly, the sufficient condition is given for the mean-square admissibility of stochastic T–S fuzzy singular systems based on an extended quadratic Lyapunov function approach. Secondly, two sufficient conditions for mean-square admissibility of closed-loop systems via the parallel distributed compensation (PDC) fuzzy controller and non-parallel distributed compensation (non-PDC) fuzzy controller are proposed. Furthermore, through the extended quadratic Lyapunov function method and non-PDC fuzzy controller, the less conservative mean-square admissibility conditions on solving fuzzy controllers are derived in terms of linear matrix inequalities (LMIs). Finally, some simulation examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology. [ABSTRACT FROM AUTHOR]