The Study Of Resilient Control Theory For Time-Delay Systems

Robust stability analysis and controller design had been the main topic in robust control theory. But most of researches at present have paid their attention to the design on the assumption that controllers can be implemented exactly. In fact, this assumption could not be true due to the imprecision inherent in analog-digital conversion, finite word length and so on. Therefore, the resilient controller, namely, non-fragile, has received more and more attention. And further investigation of this problem can not only perfect the theory basis of control systems, but also propel the application in practice. The resilient controllers design in time-delay system, and complex large-scale systems are proposed. The main results of this thesis are expressed as follows:Firstly, the resilient controller design for SISO systems is presented. Based on L-K function, bound real lemma and traditional quadratic stable conditions, sufficient conditions for system stability are given. And under two classes of perturbations, corresponding controller designs are presented. Then this method has been introduced to discrete time-delay systems.Secondly, the decentralized stable condition and corresponding resilient controller design for a class of discrete large-scale time delay systems are addressed, which is firstly introduced to large-scale systems.Thirdly, the non-fragile controller design for a class of stochastic systems is discussed. By several mathematic methods such as Markov chain and stationary transition probabilities, the sufficient condition for system stability with minimal cost is derived by sliding switch between models and controllers.Finally, considering uncertainty forms, the robust adaptive resilient controller designs are presented. By adaptive approach, the controller design can be tuned on-line. To compare the dynamic performance and cost function under unknown uncertainties with that under known, numerical example are given and illustrates the effectiveness and availability for the design.