Stability Analysis And Design For Several Classes Of Switched Systems

The dissertation investigates analysis and synthesis problems for several classes of switched systems. Focusing on the problems of output feedback controllers and filters design for switched systems, and the admissible control and the elimination or minimization of inconsistent state jumps on switching points for switched singular systems and impulsive switched singular systems. Applying switching technique to the analysis of stability and L2-gain for a class of faulty systems. The main work are summarized as follows.Two new approaches of designing output feedback controllers are proposed. One is that decoupling the bilinear inequality containing Lyapunov matrix and out-put feedback gain matrix by introducing auxiliary matrix variable. This has Lya-punov matrix and output feedback gain matrix solved individually, which brings more larger freedom of solving output feedback controllers. Using this method com-bined with multiple Lyapunov function method, the conditions of stability of the closed-loop switched system are obtained and a static and dynamic output feedback controller can be solved from these conditions. The other is that using Projection lemma and Finsler’s lemma combined with linear matrix inequality (LMI) technique, the sufficient conditions of guaranteeing admissibility of the closed-loop system as well as a desire H∞performance level are given. The conditions are proposed by the two approaches in terms of linear matrix inequality. They are very simpler-to-solve, moreover, fixing the structure of Lyapunov matrix on a certain special structure is not required and the decomposition of Lyapunov matrix and its inverse matrix is not needed. When the switched singular system reduces a single singular system or normal switched system, the design method of output feedback controllers is also available.The fault-tolerant H∞filter design is studied for switched system with sensor failures. Unknown-but-bounded fault matrix is transformed into a class of dynamic interval matrices. The scheme not only enlarges the admissible failures range of sensor but also reduces computational cost. When all subsystems exist a common Lyapunov function, a fault-tolerant H∞filter is established under arbitrary switch-ing. Even if the switched system contains unstable subsystems, a stable filtering error dynamics also can be obtained by using multiple Lyapunov functions tech-nique and constructing appropriate switching strategy.The admissible control problem is investigated for switched singular systems. In the meantime, the state jumps resulting from inconsistent initial condition when two singular subsystems switch are taken into account. An explicit formula for jumps vector at switching points is given. A hybrid impulsive controller is designed, under which the closed-loop system can be admissible as well as eliminating or minimizing the inconsistent state jumps as soon as possible. By norm consistency principle and triangle inequality, the problems of minimizing the Frobenius norm of jump vector and the upper bound of quadratic cost function are turned into a convex optimization problem containing linear matrix inequalities constraints. A lower guaranteed cost function upper bound and jumps and a suboptimal guaranteed cost state feedback controller are obtained by solving the optimization problem.A new algorithm is presented to design an impulsive controller and a feedback controller for a class of impulsive switched singular systems. The sufficient condi-tions are given, under which the closed-loop impulsive switched singular system is admissible and has no inconsistent state jumps at switching points. By decomposing matrices and substituting variable appropriately, these sufficient conditions can be converted to linear matrix inequalities.Possible faults of sensors, actuators and/or controllers for a system are con-sidered simultaneously. Inspired by switching technique, the faulty systems are regarded as a switched system. The system encountering serious failures is regarded as an unstable subsystem, in the meantime, the system encountering tiny failures is also regarded as a stable subsystem. An average dwell time method and piece-wise Lyapunov function method are adopted. The conditions of average dwell time and activation time ratio between stable subsystems and unstable subsystems are derived. When these conditions are satisfied, the switched system not only ensures exponential stability but also preserves a weighted L2-gain.Finally, the work of the dissertation is summarized and the research direction of further work is proposed.