Robust Variance Constrained Control And Filter Design For Time-Delay Systems

Time-delays are frequently encountered in the behavior of many physical processes and very often are the main cause for poor performance and instability of control systems. In view of this, the control issue of time-delay systems is a topic of great practical importance which has attracted a great deal of interest for recent years. Specially, neutral delay systems have come to a hotspot of control field and are increasingly highlighted for special attention, which concern not only previous dynamic states but also their differential states. However, the development of neutral systems is relatively slow and the references are fewer. The main reason is that difference operator of the neutral system is so difficult to deal with that the properties of the solutions to neutral systems are more complicated than those normal delay systems. Neutral delay systems extensively exist in practical engineering, so the relative investigation is quite necessary for theoretical requirement and application. And this thesis mainly investigates feedback control and filtering problem of neutral delay systems and discrete delay systems.The thesis principally applies Liapunov's second method and the variance control theory on the base of LMI in Matlab to a variety of delay-time systems, taking variance constrained and filtering into account and finally derives the existence conditions of such controllers and filters. The whole thesis mostly consists of two parts and details as follows:The first part mainly investigates robust variance constrained control for various delay-time systems. On the one hand, the problem of robust variance control for neutral systems, taking parameter uncertainties and time-delay into account, is researched. The delay-independent sufficient condition that guarantees the system to meet the variance-constrained and asymptotically stable is obtained. Based on it, linear matrix inequality technology is adopted to obtained controller. Furthermore, a numerical example is given to illustrate the effectiveness of the proposed approach. On the other hand, this thesis works over the problem of robust variance control for neutral systems, taking parameter uncertainties and nonlinearities into account. The purpose of this considered problem is to design a static state feedback controller, such that not only the steady-state variance of each state is not more than the individual pre-specified value but also the resulting closed-loop system is asymptotically stable simultaneously. And also, this thesis studies the problem of robust variance control for discrete systems, taking parameter uncertainties and nonlinearities into account. The purpose of this considered problem is to design a static state feedback controller, such that not only the steady-state variance of each state is not more than the individual pre-specified value but also the resulting closed-loop system is asymptotically stable simultaneously.The second part primarily focuses on robust filtering for neutral delay systems with norm-bounded parameter uncertainty. The addressed problem is to design a Kalman filter such that the resultant error system is asymptotically stable and the effect of the noise on the estimation error is attenuated to a prescribed level. Sufficient conditions for the solvability of the robust Kalman filtering problem are obtained in terms of LMIs. Furthermore, a numerical example is given to illustrate effectiveness of the proposed algorithm.