Study On Guaranteed Cost Control For Uncertain Systems

Based on the linear matrix inequality (LMI) method, Lyapunov stability theory and technique of inequality transformations, the guaranteed cost control problems are investigated for uncertain large-scale interconnected systems, uncertain time-delay systems, uncertain singular time-delay systems and uncertain singular time-delay markovian jumping systems. The main contents of this dissertation are written as follows:(1) The optimal guaranteed control for large-scale interconnected system with uncertain value bound is discussed. In terms of LMI, a sufficient condition for the existence of the optimal guaranteed cost state feedback controller is presented. The design of the optimal guaranteed cost state feedback controller is formulated as the problem of solving a set of LMI. Based on convex technique and homotopy method the iterate LMI method is proposed. The iterate LMI method is designed at the point of the considered system, and a new rule for choosing weighting matrix is given. Thus less conservatism in designing controller and the excellent upper bound of the linear quadratic regulator are obtained. Finally, some numerical examples are given to demonstrate the effectiveness and less conservatism of the presented method.(2) An improved inequality is proposed for robust stabilization and guaranteed cost control with parameter uncertainties. The new inequality is the improvement of the inequality which is widely used in bounding uncertainties of uncertain systems. Using this new inequality, the new criteria for robust stabilization and guaranteed cost control are derived for uncertain systems in terms of LMI. Then the method is presented for desinging the guaranteed cost controller of uncertain time-dealy system. The improved inequality has less conservatism, which is demonstrated by some numerical examples in uncertain time-delay systems, uncertain discrete-time systems and uncertain singular time-delay systems.(3) The effects on system performance arising from the uncertainties of both the system matrix parameters and the controller are considered. In terms of Linear Matrix Inequalities (LMIs), a design method of the observer-based non-fragile guaranteed cost controller is obtained by constructing generalized Lyapunov function and generalized quadratic regulator on the basis of Lyapunov stability theory. By using the designed controller, not only the stability of the uncertain singular time-delay system is guaranteed, but also the upper bound of quadratic guaranteed cost function is obtained. A new method is approached to design the non-fragile guaranteed cost controller and obtain the observer matrix. It's also shown that these conditions are equivalent to the solvability of two groups of strict LMIs. Finally a numerical example is given to prove the validity of the proposed method. (4) For Markovian jumping systems have the advantage of better representing physical systems with abrupt variations, and singular time-delay systems can describe physical systems better than state-space ones, the delay-dependent guaranteed cost control (GCC) problem for uncertain singular time-delay systems with Markovian jumping parameters is concerned. In terms of LMI approach, the sufficient conditions are proposed for singular Markovian jumping systems with time-delay to be stochastically admissible. Based on the conditions presented, the sufficient conditions are obtained for the existence of guaranteed cost controller, which guarantees the uncertain singular Markovian jumping systems with time-delay to be regular, impulse free and stochastically stable and the quadratic cost function smaller than an upper bound. The explicit expression of the guaranteed cost controller is also characterized by solving a set of LMIs. Numerical example is given to show the effectiveness of the proposed method.