Guaranteed Cost Control For Uncertain Singular Bilinear Systems

The stability and performance are mostly concerned in the control system. Uncertain phenomenon exists commonly in the practical application of the control system. It is one of main factors that affects the system’s stability and performance. In recent years, uncertain system has aroused wide attention by theoretical and practical workers. The robust guaranteed cost control is try to describe the uncertainty of the controlled object, it is also try to integrate the controller in the allowed disturbance range of uncertainty, and guarantee the stability of system whose quadratic performance index less than the upper bound. Singular bilinear system can describe more accurately industrial objects, which becomes a powerful tool for depicting the characterization of some practical systems. Therefore, the research of singular bilinear system has important theoretical significance and practical application valueless.In this thesis, we consider the guaranteed cost control of uncertain singular bilinear systems with uncertain parameters in the two situations of the norm-bounded and meeting the matching condition, based on the research condition of singular, bilinear, uncertainty system theory. On the one hand, based on theory of Lyapunov stabilization, the sufficient condition of guaranteed cost control for singular bilinear system with uncertainly is presented by using the method of linear matrix inequality and applying the method of enlargement in the set domain simultaneously. On the other hand, the design method of a state feedback guaranteed cost controller which makes the closed-loop system stable is illustrated. The main contents and results are summarized as follows.(1) We expand the guaranteed cost control theory of uncertain normal system to singular system. Then, the guaranteed cost controls of two different uncertain singular systems are discussed respectively.(2) We consider the robust guaranteed cost control of two different uncertain singular bilinear systems, which based on the different situations that the uncertain satisfied. Then, we design the state feedback guaranteed cost controller. Finally, we respectively present the sufficient conditions of robust guaranteed cost control of the closed-loop singular bilinear systems which under the condition that the uncertainty is norm-bounded and the uncertainty goes with the matching condition.