Filtering For Discrete-Time Switched Systems With Delays

The measurement error and random disturbance are often encountered in the practicalsystems. How to extract the useful signals from the original signals with noise can be consideredas the filtering problem.The switched systems are a special class of hybrid systems. There are more and moreproblems involved in the switching in practice. The filter design of the switched systemsbecomes very difficult due to the extensive existence of the time delays and disturbance.Therefore the research on filtering for switched systems with delays has great significance intheory and applications.Based on the piecewise Lyapunov-Krasovskii functional, Jensen inequality, extendedH（o|¨）lder-Minkowski inequality and slack variables, this dissertation discusses the filtering for thediscrete-time switched systems with delays. The main contributions of this dissertation are listedas follows:（1） The generalized H₂filtering problem is investigated for the linear discrete-time switchedsystems with multiple time-varying delays. By constructing the piecewise Lyapunov-Krasovskiifunctional, employing Jensen inequality and slack variables, the delay-dependent sufficientconditions are derived for the filter-error system to be stable with the H₂performance underarbitrary switching signals. Based on the established results, the filter design method is presentedin terms of the Linear Matrix Inequality （LMI）. The optimal solution of the generalized H₂filtering performance and filter parameters are obtained.（2） By considering two different types of disturbance signals with energy-bounded andknown statistical properties in the systems, the mixed H₂/H_∞filtering problem is investigated forthe linear discrete-time switched systems with multiple time-varying delays. In view of H₂andH_∞performance channels, the delay-dependent sufficient conditions are developed respectively.Then the sufficient conditions can be obtained for guaranteeing the asymptotic stability of thefiltering error systems with the mixed H₂/H_∞performance. Based on the above, the filter designmethod is presented to solve the optimal filter performance and the corresponding filterparameters. （3） The generalized H₂filtering problem is considered for the discrete-time switchedsystems with infinite distributed delays. By constructing the piecewise Lyapunov-Krasovskiifunctional, employing extended H（o|¨）lder-Minkowski inequality and slack variables, the sufficientconditions are derived for the filter-error system to be stable with the generalized H₂performance and the optimization filter is synthesized.