Robust Filtering For Markov Jump Systems With Time Delay

Recent years have witnessed the development of the research work on the robust fil-tering for Markov switching systems with state delays. Notable results have been achievedin terms of the research on the design of robust filters for continuous-time Markov sys-tems with the help of LMI techniques, while discrete-time Markov jump systems receivedless attention to our best knowledge. It is worth pointing out that discrete-time Markovjump systems can be proposed to describe and represent a large amount of models inpractical industrial processes with abrupt structure parameters. The robust filter analysisand synthesis problem of this kind of Markov jump systems are presented as follows.A new mode-dependent Lyapunov-type functional for the filtering error system isfirstly constructed. And the functional includes the necessary time delay informationand jumping parameters of this kind of system. When treating with diferences of theLyapunov functional, the classical Jesen’s inequality is integrated with a novel reciprocalconvex combination technique. This difers from those traditional methods in dealingwith time-delay using free-weighting matrix or delay partitioning.Based on the new technique and taking the jumping parameters into account, the im-proved sufcient conditions for the stochastic stability of the filtering error systems andparameterization of the desired robust H∞, l2l∞and passive filters depending on theswitching mode are established in terms of a series of feasible LMIs, which can be trans-formed into the corresponding convex programming problems as well. Furthermore, therobust filter design results are applied to systems subject to polytopic type uncertainties.In addition, each chapter presents a series of specific experimental examples to ver-ify the applicability and validity of the creative approaches.