Theoretical Study On Robust Stability For Several Classes Of Discrete Systems Based On LMI

With the successful application of linear matrix inequality (LMI) to the research of robust control, many internal and oversea scholars intend to transform the robust stability and robust performance of uncertain systems into solving the problems of LMI. The robust stability of several classes of uncertain discrete systems is studied in this dissertation, by using LMI as tools to find the proper Lyapunov functions. The problems of robust stability for these uncertain systems are transformed into finding a feasible solution of LMI. The major contributions of this dissertation are as follows:1. The robust stability is studied for a class of discrete systems with the nonlinear perturbations. By using the LMI as tools, the robust stability conditions of these systems are provided. On the basis of these, the way to design the state feedback controller of these systems is proposed in the form of LMI. The state feedback controller can be obtained by solving an LMI. Furthermore, the way to design the state feedback controller is studied for a class discrete system with nonlinear coupled perturbations of system inputs and system states. Then, the stability of interval discrete systems is researched. Using LMI technology, the sufficient and necessary stability conditions of these systems are given subject to the uncertainty of state space models.2. Discrete systems generally have the coupled perturbations of current state and past state. So, the robust stability is studied for a class of time-delay discrete systems with perturbations of current state and past state. The robust stability conditions are concluded based on the Lyapunov Second Method. On the basis of these, the way to design the state feedback controller is provided for these uncertain tune-delay discrete systems. Then, the robust stability is studied for a class of multi-delay discrete systems with nonlinear coupled perturbations of current state and past states. The sufficient stability conditions are proposed in the form of LMI, and the design procedure of state feedback controller is given based on these stability conditions.3. The stability problems of FMM II model of 2-D systems are investigated by using LMI, and some new criteria for asymptotical stability of the systems are given. On the basis of these criteria, the robust stability is studied for a class of uncertain 2-D systems. The robust stability conditions are provided in the form of LMI subject to the uncertainty of these systems. And the algorithm for designing the state feedbackcontroller is presented, too. It is shown that designing the state feedback controller of these systems can be formulated as a convex optimization with LMI constraints.4. The dynamic matrix control algorithms based on finite impulse response are studied. The model errors are defined in the form of upper and lower bound and the error square sum of impulse response coefficients of single-input/single-output systems. The robust stability conditions are proposed for closed-loop systems using DMC in the form of LMI, which can assure the closed-loop system using DMC algorithm to be asymptotically stable, when the coefficients of characteristic polynomial don't satisfy Jury's dominant coefficient lemma. Then the model errors of multi-input/multi-ourput systems are defined for the in the form of square sum of impulse response error matrix 2-norm.The stability conditions are provided for these systems using DMC algorithm.5. The singular systems are different from general discrete systems. So theregularity, causality and stability(RCS) are all considered, when the properties of singular systems are studied. The robust property of RCS is studied for a class of uncertain singular discrete systems. The robust RCS conditions of these systems are proposed. Then, the robust property of RCS is studied for a class of time-delay singular discrete systems with perturbations of delay parameter jump. The robust RCS delay-dependent conditions of these systems are provided in the form of LMI.