Finite-time dissipative filter design for discrete-time stochastic interval systems with time-varying delays

Abstract

The finite-time dissipative filtering problem for a kind of discrete-time stochastic interval system with time-varying delays whose parameters are taken in a convex hull is investigated in this paper. Taking a representative subsystem from a stochastic convex hull system, based on convex analysis and matrix theory, a new interval matrix method is proposed to study the finite-time dissipative filter problem, which can deduct the conservativeness. Then, the finite-time dissipative filter is designed by employing a complex Lyapunov-Krasovskii functional together with the improved Wirtinger inequality technique. Correspondingly, some novel sufficient conditions are obtained to ensure the filtering error system with time-varying delays robustly stochastically finite-time bounded and the dissipative index is satisfied. Next, the desired filter gains are achieved in terms of linear matrix inequalities. Finally, the effectiveness of the designed filter is demonstrated by a numerical example with simulations.