It is almost impossible to obtain an accurate mathematics model for the practical industrial process. Therefore, the model-based modern control theory is hard to use to analyze and synthesize a practical control system. The model uncertainties of systems will be a main cause of bad performance or even instability for control systems. On the other hand, time-delay exist in many systems such as steel rolling, transmission process, and network signal transmission et al. The existence of delay makes system analysis become more complicated and difficult, Meanwhile, delay is frequently a source of instability and performance degradation in many dynamic systems. Therefore the study of the uncertainty systems with time-delay has theoretic and practical significance, and has attracted considerable attention in the control theory literatures.Presently, although there are many results about these problems, lots new problems still need much study and research. In this dissertation, based on Lyapunov stability theory, through using linear matrix inequality as main mathematical tools, we study the robust Hâˆžcontrol problem of uncertain time delay system described by state space model with time delay and multiple time delays. The major contributions are as follows:(1) Study the control problem of state time delay uncertain system described by state space model. A sufficient condition for the solvability of the robust Hâˆžguaranteed cost control problem was presented and proved by applying a proper Lyapunov function and linear matrix inequality. A robust Hâˆžguaranteed cost controller which satisfies proper performance was designed.(2) Study the control problem of sate and input time delays uncertain system described by state space model. A sufficient condition for the solvability of the robust Hâˆžguaranteed cost control problem was presented and proved by applying a proper Lyapunov function and linear matrix inequality. A robust Hâˆžguaranteed cost controller which satisfies proper performance was designed.(3) Deal with a problem of a class of complex uncertain system with multiple time delay under controller gain perturbations. A sufficient condition for the solvability of the non-fragile robust Hâˆžguaranteed cost control problem is proved and presented by applying proper Lyapunov function and linear matrix inequalities. The non-fragile robust Hâˆžguaranteed cost controller was designed. |