New results on H∞ filter design for time-delayed discrete-time system with nonlinear sensors

This paper investigates the filtering problems of the time-delayed discrete-time systems with saturation nonlinear sensors, in which process and measurement noise have unknown statistic characteristic but bounded energy. Base on the H∞ performance analysis of filtering error systems, the filters are well designed for the discrete-time systems with time delays and saturation nonlinear sensors to guarantee the asymptotic stability of the error systems and reduce the effect of the noise signals on the filtering error to the lowest level. A numerical example is given to demonstrate the effectiveness and applicability of the proposed design approaches.

1 Introduction

The filtering problem is to design an estimator to estimate the unknown state combination via output measurement, which guarantees the L2 gain (from the external disturbance to the estimation error) less than a prescribed level [1]–[7]. In contrast with the well-known Kalman filter, the filter does not make any assumptions about the statistics of the process and measurement noise (although this information can be used in the filter if it is available), but only assumes the external disturbance to have bounded energy. The filtering technique has been found useful in industrial applications. One of such applications is reported in [7] for seismic signal deconvolution. Various filter design approaches, such as the algebraic Riccati equations, interpolation, linear matrix inequality (LMI) and so on, to have been successfully proposed and many results on this topic have been reported in the literature [1]–[7].