H∞ filtering for uncertain systems with time-delay and randomly occurred sensor nonlinearities

Abstract

This paper investigates the H∞ filtering problem for discrete time-delay systems with quantization and stochastic sensor nonlinearity. The problem of quantization considered in this paper is logarithmic quantization and the quantization error is processed into an uncertain term. The sensor nonlinearity is supposed to occur randomly on the basis of a stochastic variable obeying the Bernoulli distribution and the nonlinear decomposed technique is introduced to deal with the nonlinear term. The time-varying delay of systems is processed by using the Scaled Small Gain (SSG) theorem. The LMI-based sufficient conditions in view of the SSG and the Lyapunov–Krasovskii functional (LKF) approach are presented to guarantee the error system mean square stable and with the prescribed H∞ performance index γ. An example is given to illustrate the effectiveness of the proposed method.