Resilient Guaranteed Cost Control And Robust H_∞ Control For Switched Singular Systems

This thesis devotes to the study of resilient guaranteed cost control and robust H∞control for the uncertain switched singular systems. The uncertainty of the system describes the difference between the mathematic model and controlled plant, which reflects the existing of the variation of the system parameters and disturbance. Meanwhile, delay is frequently a source of instability and performance degradation in many dynamic systems. Thus for switched singular systems with uncertainty and state delay, using Lyapunov method, and matrix inequality etc, this thesis has given a further investigation about the stability analysis, resilient guaranteed cost control and robust H∞control problems of the systems.The main contents of this thesis are as follows:(1) Firstly, for a class of switched linear singular systems with state delay, the problem of designing asymptotically stabilizing state feedback controllers and output feedback controllers are investigated. The sufficient conditions for existence of such controllers are derived by the common Lyapunov function technique and the corresponding switching laws are constructed to guarantee stability. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.(2) Secondly, the problem of resilient guaranteed cost control is studied via state feedback for a class of uncertain switched singular systems. The sufficient conditions which make the resultant closed-loop switched singular systems not only quadratic stable but also have the upper bounded of the cost function are proposed in terms of linear matrix inequality (LMI) technique. Moreover, the resilient guaranteed cost controller can be obtained by solving the linear matrix inequalities. The designed resilient controller can make the closed-loop systems to be quadratic stable and the closed-loop cost function value have an upper bound. A numerical example is given to illustrate the validity of the proposed method.(3) Lastly, the design problem of robust H∞state feedback controller is investigated for a class of uncertain switched singular systems with state delay. Based on common Lyapunov function approach and convex combination technique, the sufficient conditions for the existence of sub-controllers are presented in the form of matrix inequalities. And both sub-controllers and switching laws are designed. By using eliminated element method, the matrix inequalities are transformed into linear matrix inequalities. A numerical example is employed to illustrate the correctness of the corresponding results.