Robust H _∞ Filter for Markovian Jump DOSs with Time-Varying Delays

Introduction

Recently, the problems of the filtering has been studied by a number of authors, see for example [9, 71, 72, 178] and the references therein. Both a Kalman-filter-based iterative algorithm and a recursive frequency estimator using linear prediction have been considered in [305]. In [122], the synthesis of two observer-based nonlinear control algorithms was performed within the globally linearizing control framework. A problem of optimal linear Kalman filtering with packet losses has been considered in [109]. When parameter uncertainty arises in a system model, the robust H _∞ filtering problem has been studied in [75]. Because H _∞ filtering provides a bound for the worstcase estimation error without the need for knowledge of noise statistics, it has been demonstrated that H _∞ filtering has the advantage of being less sensitive to uncertainties of the underlying system. The class of Markovian jump systems is an important family of systems subject to abrupt variations. The Markovian jump systems have finite modes, which may jump from one to another at different times and between different modes. A system with such a “jumping” character may be modeled as a hybrid system, and the parameter jumps among different modes can be seen as discrete events. Note that the concept of Markovian jump filter has already been used in some papers, for example [6, 20, 209, 275]. Robust Kalman filtering for continuous systems with Markovian jumping parameters was given in [160, 208].