Robust Control Of Uncertain System With Delays

Since the naissance of modern control theory at the end of 19'50, the control theory has got far development. Much result of the modern control theory is based on the accuracy math model. However, most of model on control object are uncertainty. That because it's unavoidable to include uncertain parameters and disturbance in practical control systems due to the modleing errors, measurment errors, linearization approximation and so on. Meantime, there are problems on the varying of the entironment and the ageing of the apparatus. On the other hand . owing to the improvement of studying methods and the increasing need for high accuracy and design in systems, uncertainties, which are neglected conventional study, have to be taken into account, and attract more, attention. Therefore, it is important to study the control problem of uncertain systems. As is known to all that delay is common in the process of practical control. The reasons as follows:(l). the transmission of material and signal,(2). the measurement of system signal,(3).some property of apparatus. Time-delay system can be regard as infinit- dimension system and the controller design is more complicated than the systems without delays. The systems are often destabilize due to the existence of delay. Hence, there are much important theory and practical value on the study of robust control on time delay system with uncertainties.The dissertation are mainly on the study of the robust control on the uncertain system with delays. The organization of this dissertation is as follows:In chapter two. the problem of robust tracking and model following is considered for a class of linear system with delay and uncertainties. The uncertainties are composed with three parts: one is norm bounded uncertainties, one is matched uncertainties, the last is unknown disturbance which is bounded.We first define a error system and then the problem of robust tracking and model following is transformed to the problem of design robust controller such that the error system is stabilized. Based on Lyapunov stability theory, the corresponding control strategy are adopted to design robust controller with respect to different characteristics uncertain and disturbance. Combining with the method of LMI and the method of adaptive parameter estimation .delay-independent and delay-dependent controllers are designed respectively which can make the closed-loop error system ultimately uniformly bounded or asymptotically to zero. and the result of delay-independent is extended to interconnected large-scale systems.It deserve to point out that the delay-dependent controller by the descriptor transform can make the state of the closed-loop error system asymptotically to zero. The main contribution of this part is that the designation of controller The closed-loop of error system is uniformly ultimately boundedor asymptotocally stable when the disturbance is not satisfying matched conditions.In chapter three,the problem of robust stabilization is considered for uncertain nonlinear system with delays. It consists of three parts. One part is a essential nonlinear .system with mismatched delay disturbance. A new Lyapunov function is constructed for the system with disturbance. Based on the constructed Lyapunov function, the robust controller is designed which can make the closed-loop system exponential asymptotically stable. One part is a essential nonlinear system with delays. Enlightened by the definition of CLKF, a new Lyapunov functional is constructed by adding to some non-negative functional on the known Lyapunov functional. On the other hand, the system's state may not be got by some reasons. Then the state feedback is out of effect. Therefore, the last part is the problem of robust control by output feedback for a nonlinear system with delay disturbance. The main contribution of this part is as follows: â‘  the controllers designation of the disturbance system. In the past, the controllers designation oi the nonlinear system with delays and disturbance is based on the Lyapunov function of the nomin...