Robust Control Of Linear Uncertain Systems

It is almost impossible to obtain an accurate mathematics model for the practical industrial process. The model under which the controller is designed is usually different to the real plant owing to model reduction; linearization approximations; unrnodeled dynamics; the change of the operating environment; measurement errors; unmeasureable disturbances; and so on. Therefore, Based-model the modem control theory is hardly used to analyze and synthesize a practical control system. The differences can be described as the model uncertainties. 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 frequently a source of instability and deterioration of system performances, so the study of delay systems always attracts considerable attention in the control theory literature. Therefore, the robust performance analysis and synthesis problem of uncertain systems, particularly, time-delay uncertain systems, will be mainly studied in this dissertation.Based on Lyapunov stability theory, through using linear matrix inequality and matrix analysis as the main mathematical tools, this dissertation studies the robust control problem of systems described by state space equation with norm-bounded timevarying 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). Given a quadratic performance function, designing state feedback guaranteed cost control laws are studied for a class of uncertain linear systems with both state and control delays, and with 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.(2). By using the linear matrix inequality approach, the delay-dependent guaranteed cost control problem for a class of linear uncertain time-delay systems is studied. The existence conditions are derived and a parameterized representation of theIllABSTRACTdelay-dependent guaranteed cost controllers is presented. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller.(3). The decentralized stabilization problem of interconnected continuous/discrete linear systems with delay is studied. Sufficient conditions for the existence of the decentralized stabilizing state feedback controllers are given in terms of some linear matrix inequalities (LMIs). Furthermore, convex programs are formulated to design a decentralized stabilizing controller with low feedback gains. Chapter 4.3 focuses on the design problem of decentralized guaranteed cost state feedback controllers for a class of interconnected uncertain discrete-time systems and a given quadratic cost function. By using the linear matrix inequality (LMI) approach, sufficient conditions for the existences of the decentralized controllers are derived, and a parametrized characterization of a set of decentralized guaranteed cost controllers are provided. Furthermore, a convex optimization problem is formulated to select the optimal decentralized guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.(4). The output feedback guaranteed cost control problem is studied in this paper for uncertain discrete-time systems. 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...