Robust Estimation For Linear Uncertain Time-Delay Systems

Motivated by the successful application of LMI techniques to robust analysis and synthesis of linear time-invariant systems, many scholars have devoted their efforts by applying the same techniques to robust analysis and synthesis of linear time-delay systems. There are two reasons for this motivation. One is the existence of quick and effective numerical algorithms. The other is that LMI can describe different kinds of convex constraints. Due to the inherent complexity of linear time-delay systems, there lacks a general framework to the analysis and synthesis of such systems. When applying some existing methods, the obtained results may be a bit conservative. In this dissertation, upon the deeper analysis of robust estimation for linear time-delay systems, the LMI approaches of robust filter designs are proposed. The main research results in this dissertation can be given as follows.1) A design of unknown input observer for a class of linear time-delay systems is proposed. The objective is to design an observer such that estimation error can be completely decoupled from the unknown input (disturbance or fault). The cases the observer error is stable asymptotically or exponentially are considered. Two design problems of the observers with and without internal delay are formulated. The unknown input observer with H∞performance is dealt with when the observer error can not be completely decoupled from the unknown input. Based on Lyapunov stability theory, existence conditions of such observers are derived. Filters are designed in terms of linear matrix inequalities. Filters gain matrices are easily obtained by using MATLAB LMI toolbox.2) Robust guaranteed cost filtering, L2 ? L∞filtering, passive filtering, dissipative filtering for a class of linear uncertain time-delay systems are proposed. The objective is to design linear filters such that for all uncertainties, the filtering error system is robustly stable and satisfies the proposed performances. Based on Lyapunov stability theory, existence conditions of filters are derived. Filters are designed in terms of linear matrix inequalities.3) The results on robust filtering for linear uncertain time-delay systems are extended to linear uncertain descriptor time-delay systems. Robust guaranteed cost filtering, passive filtering, dissipative filtering are studied for such a kind of systems. The objective is to design linear filters such that for all uncertainties, the filtering error system is regular, impulse-free, robustly stable and satisfies the proposed performances. Based on Lyapunov stability theory, existence conditions of such filters are derived. Filters are designed in terms of linear matrix inequalities.4) Based on Lyapunov stability theory, the results on robust filtering for linear uncertain time-delay systems are extended to linear uncertain neutral delay systems. Robust guaranteed cost filtering, passive filtering and dissipative filtering are studied. The objective is to design filters such that for all uncertainties, the filtering error system is robustly stable and satisfies the proposed guaranteed cost, passive and dissipative performance, respectively. Filters gain matrices are obtained by solving LMI.