H_∞ Optimal Control Of Impulsive Switched System And Application

H_∞optimal control as an important part of system control theory and system engineering attracts more and more interests of scientists who study control and system engineering. H_∞optimal control theory is one of efficient methods to enhance system robust. In the late 20 years the H_∞control theory developed quickly. On the other hand, in recent years, hybrid (switched) system and impulsive hybrid (switched) system are attractive lately and attract lots of scientists who studies applied mathematics, computer science, system engineering, etc, which bring chances and challenges for control theory and system engineering. H_∞optimal control theory of impulsive switched system and application of impulsive control are studied. Firstly, H_∞optimal control problem of linear impulsive dynamic systems is studied. Then H_∞optimal control problem of linear impulsive switched system is studied and the corresponding control laws are obtained. Then, the H_∞optimal control problem for nonlinear impulsive switched systems with norm-bounded time varying uncertainty is considered. Based on the Riccati inequality approach, we derive the sufficient conditions of robust H_∞stability of nonlinear impulsive switched systems and present linear time invariant state feedback control laws to stabilize those systems. The robust stability and stabilization problem for a class of impulsive switched systems with uncertainty is studied. We develop the sufficient conditions of the impulsive switched systems' uniform asymptotical stability and give linear time invariant state feedback control laws, which can robustly stabilize the impulsive switched systems by using linear matrix inequalities method. Futhermore, it is concerned with robust stability problem for impulsive switched system with LQ guaranteed cost control. Some results for robust stability of this class of impulsive switched system are obtained. Sufficient conditions for existence of guaranteed cost controller are given. Under these conditions the guaranteed cost controller also guarantees the robust stability performance of uncertain impulsive switched system. The problem of robust H_∞stabilization with definite attenuance for a class of impulsive switched systems with time-varying uncertainty is discussed. A norm-bounded uncertainty is assumed to appear in all the matrices of the state model. A LMI based method for robust H ∞stabilization with definite attenuance via state feedback control law is developed. A simulation example is presented to demonstrate the effectiveness of the proposed method. For impulsive robust stabilization problem of nonlinear systems, criteria for impulsive robust stabilization are obtained, and the corresponding impulsive controllers are given. We use Simulink toolbox of Matlab to simulate Lüchaotic systems, and it shows impulsive control is an effcient method to stabilize chaotic system with uncertainty. The robust stabilization of Chen's chaotic system is studied. By employing impulsive control approach, Chen's chaotic system with uncertain disturbance is controlled to the equilibrium point. Sufficient conditions of robust stabilization and robust synchronization of Chen's chaotic systems are obtained by asymptotically stabilize error system of impulsive synchronization between two Chen's chaotic systems. By employing the result of H ∞optimal control of nonlinear impulsive system, impulsive feedback H ∞robust stabilization of Chen's system is studied and numerical simulation is given. Finally, a summary has been done for all research work in the thesis. The research work in further study is presented.