Robust H_∞ filtering for discrete nonlinear delayed stochastic systems with missing measurements and randomly occurring nonlinearities

Abstract

In this paper, we are concerned with the robust filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under consideration involves parameter uncertainties, stochastic disturbances, time-varying delays and sector nonlinearities. Both missing measurements and randomly occurring nonlinearities are described via the binary switching sequences satisfying a conditional probability distribution, and the nonlinearities are assumed to be sector bounded. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the filtering error is constrained to be robustly exponentially stable in the mean square, and a prescribed disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality. Finally, a numerical example is exploited to show the usefulness of the results derived.

Keywords:

• filtering
• missing measurements
• randomly occurring nonlinearities
• time-varying delays
• Lyapunov–Krasovskii functional
• linear matrix inequality

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61374010], [grant number 61074129], [grant number 61175111]; the Natural Science Foundation of Jiangsu Province of China [grant number BK2012682]; the Qing Lan Project of Jiangsu Province (2010); the 333 Project of Jiangsu Province (2011); the Six Talents Peak Project of Jiangsu Province (DZXX-047, 2012).