Filter Design Of The Delay Systems With Markov Switching Parameters

In this dissertation, we consider the special time-delay systems with Markovian switching parameters. The main results can be listed as follows:In the first part, the problem of L₂ - L_∞filter for a class of Markov jump system with delays is considered. Attention is focused on the design of full-order and reduced-order filters guaranteeing a prescribed L₂ - L_∞performance for the filtering error systems. Both delay-independent and dependent approaches are presented. Sufficient conditions for the existence of the filters are expressed in terms of a set of strict linear matrix inequalities (LMIs). The explicit parametrization of the desired filter is also given in a unified framework. Numerical example is given to demonstrate the validity of the approach.In the second part, we deal with the robust H_∞filtering problem for a class of stochastic Markovian switching system with time-delay and nonlinear disturbances. We aim at designing of full-order filter and reduced-order filter such that, for all nonlinearities and time-delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed H_∞disturbance rejection attenuation level. Sufficient conditions are established to ensure the existence of the desired filters, which are expressed in the form of linear matrix inequality (LMI). The explicit parametrization of the desired filter is also given in a unified framework. Finally, a numerical example is exploited to show the usefulness of the results derived.