The filtering problem for a class of discrete-time stochastic systems with nonlinear sensor and time-varying delay is investigated. By using the Lyapunov stability theory, sufficient conditions are proposed to guarantee the asymptotical stablity with an prescribe performance level of the filtering error systems. These conditions are dependent on the lower and upper bounds of the discrete time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods. 1. Introduction As is well known, time delay exists commonly in many processes due to the after-effect phenomena in their inner dynamics, which has been recognized to be an important source of instability and degraded performance. The presence of time delay must be taken into account in modeling due to the ever-increasing expectations of dynamic performance. Therefore, time-delay systems have drawn much attention in the last few decades, and a great number of important results have been reported in the literature; see, for instance, [1–5] and the references therein. For continuous-time systems, the obtained results can be generally classified into two types: delay-independent and delay-dependent ones. It has been understood that the latter is generally less conservative since the size of delays is considered, especially when time delays are small. Compared with continuous-time systems with time-varying delays, the discrete-time counterpart receives relatively less attention. See, for example, [6–9] and references therein. In the past few years, considerable attention has been devoted to the topic of filtering in the past two decades, and many significant results have been obtained [10–19]. The exponential filtering problem is studied for discrete time-delay stochastic systems with Markovian jump parameters and missing measurements in [20]. The robust fault detection filter problem for fuzzy It？ stochastic systems is studied in [21]. The problem of robust filtering for uncertain discrete-time stochastic systems with time-varying delays is considered in [22]. Meanwhile, in many industrial processes, the quality and reliability of sensors often influence the performance of the filters. Nonlinearity is present in almost all real sensors in one form or another. So, the filtering problem for a class of nonlinear discrete-time stochastic systems with state delays is considered in [23]. The robust filtering problem for a class of nonlinear discrete time-delay stochastic systems is considered in
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