The Robust Control For Linear Uncertain Discrete-time Time-delay Systems

The accurate mathematics model for the practical industrial process is almost impossible to obtain. Because there are usually differences between model calculation and the real plant owing to model reduction,linearization approximations,unmodeled dynamics,the change of the operating environment,measurement errors, unmeasureable disturbances,and so on. Those differences can be described as the model uncertainties. Therefore,to analyze and synthesize a practical control system using the model-based modern control theory is very difficult. On the other hand,because of pipe transmission processes, net transmission, large-lag links, etc,a large number of industrial processes can be modeled as time-delay systems. The existence of delay is usually a source of instability and deterioration of system performances,so robust control for uncertain systems have been the focus of the research in control theory. In control applications, most of computer controlled systems are sampled-data systems, so the depth research on the topic will make great contribution to the control theory. Therefore,robust performance analysis and synthesis for uncertain systems,particularly,the time delay discrete time uncertain systems,are mainly studied in this dissertation. Based on Lyapunov stability theory,using linear matrix inequality and matrix analysis as the main mathematical tools,the dissertation studies the robust control problem of systems described by state space equation with norm bounded time-varying parameter uncertainties. The robustness analysis and synthesis methods for the considered uncertain systems are developed in this dissertation. The major contributions of this dissertation are as follows: 1,Zeros of sampled continuous systems with time delay were considered in this dissertation. It is deducted in the dissertation that the zeros of the sampled system is closely related to the fractional time delay and the trajectories of the zeros presents a certain regularity as the fractional time delay changes from 0 to 1. Through the analysis on zeros of the SISO fractional time delay, detailed method of parameter identification is also given. 2,The dissertation discussed analysis and synthesis techniques for robust pole placement in LMI regions. It focused on linear systems with static uncertainty on the state matrix,the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary LMI regions. The analysis results are then applied to the synthesis of dynamic output feedback controllers. 3,The dissertation discussed the robust stability analysis and robust controller design of uncertain systems with time delay. The sufficient condition for the stability of linear uncertain systems with a time varying delay is presented by a vector inequality and the stability theory of Lyapunov. The obtained criterion includes information on the size of delay, and therefore,belongs to delay dependent criteria, therefore, the conservativeness of the controller design is reduced.. A robust control design method for parameter uncertain systems that have the delay in both state and control input is presented. Through a certain algebraic Riccati inequality approach,a state feedback controller is obtained,the result is independent on the size of delay. The Problem of robust stabilization for linear uncertain systems with states and control delays is studies. The uncertain parameters are unknown and time varying,but norm bounded and the delays are also time varying. Based on the Lyapunov function,sufficient condition for the robust stabilization via state feedback was presented in terms of linear matrix inequalities,and a memoryless state feedback control law was constructed by using the solutions of the linear matrix inequalities. 4,The dissertation gives a quadratic performance function and designs state feedback guaranteed cost control laws for a class of uncertain linear systems with both state and control delays and time-varying multi-state delays. By using the linear matrix inequality approach,the existence conditions are derived and a parameterized representation of the guaranteed cost controllers is presented. Furthermore,a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller.5,The output feedback guaranteed cost control problem of uncertain discrete time systems is studied in this paper when the uncertainty in the system is assumed to be norm bounded and time varying. This problem is to derive a design procedure for output feedback controllers that render the closed-loop system to be asymptotically stable and guarantee an upper bound of the given performance cost for all admissible uncertainties. .It is proved that the existence of the guaranteed cost control is equivalent to the feasibility of a certain linear matrix inequality(LMI),and a full order output feedback controller can be constructed in terms of the feasible solutions to this LMI.. Furthermore,a convex problem is formulated to design the optimal guaranteed cost controller that minimizes a specified cost bound . By concluding this dissertation,some perspective and consideration are given.