Delay-dependent reliable H_∞ filtering for sector-bounded nonlinear continuous-time systems with time-varying state delays and sensor failures

Abstract

In this article, the reliable H _∞ filtering problem against sensor failures is investigated for a class of continuous-time systems with simultaneous sector-bounded nonlinearities and varying time delays. The focus of this article is on designing a reliable filter such that the filtering error system is asymptotically stable and meets the prescribed H _∞ norm constraint in the normal case as well as in the sensor failure case simultaneously. Linear matrix inequality conditions, which depend not only on the upper and lower bounds of delay but also on the upper bound of delay derivative, are obtained for the existence of admissible filters and, based on these, the filter design is cast into a convex optimisation problem. What is worth mentioning is that the information about the upper bound of the delay derivative is taken into consideration even if this upper bound is not smaller than 1. A numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method.

Keywords:

• H _∞ filtering
• time delays
• reliable filter
• sensor failure
• Lyapunov–Krasovskii functional
• linear matrix inequality

Acknowledgements

This work was supported in part by the Funds for Creative Research Groups of China (No. 60821063), National 973 Programme of China (Grant No. 2009CB320604), the Funds of National Science of China (Grant No. 60974043) and the 111 Project (B08015), the Fundamental Research Funds for the Central Universities (No. N090604001).