Study On The H_∞ Control Problem For Classes Of Switched Nonlinear Systems

As an important class of hybrid systems,switched nonlinear systems are of great significance both in theory development and engineering applications.In the study of hybrid systems,the H_∞control for switched nonlinear systems is one of the most important and challenging fields.Due to the existence and interaction between the nonlinear continuous dynamics and discrete switching strategy,the behavior of the switched systems is very complicated.Many analysis and design problems deserve further investigation.This dissertation focuses on the H_∞control for switched nonlinear systems based on analysis and control synthesis of switched systems and nonlinear systems by using the Lyapunov control theory.Some theories and methods of nonlinear H_∞control problem are extended to establish a theory framework of H_∞control for switched nonlinear systems.The common Lyapunov function method,single Lyapunov function method,convex combination technique,multiple Lyapunov function method and the average dwell time method are exploited to solve the H_∞control for switched Lipschitz nonlinear systems,switched cascade nonlinear systems and switched affine nonlinear systems in presence of perturbations and uncertainties.Stabilizable and unstabilizable subsystems,measurable and unmeasurable states are allowed to co-exist,respectively.The main contributions of this thesis are as follows.1.From the fact that the system states are often not available,the observer-based H_∞control for a class of switched Lipschitz nonlinear systems is considered. Observers,observer-based output feedback controllers,and a hysteresis switching strategy depending on the observer state and the previous value of switching signal are designed simultaneously.The generalized multiple Lyapunov function method, which improves the nonincreasing requirement at switching time sequences, provides more freedom for the problems addressed to be solvable.2.When actuators suffer a "destabilizing failure" and the never-faulty actuators cannot stabilize the given system,the problem of reliable exponential stabilization and H_∞control for a class of switched Lipschitz nonlinear systems is addressed via the average dwell time approach.Since the system states are often not available, observers,observer-based output feedback controllers and switching strategies satisfying an average dwell time condition are constructed simultaneously.For the switched Lipschitz nonlinear systems with stabilizable and unstabilizable subsystems, the addressed reliable problem is solvable if the activation time ratio between stabilizable subsystems and unstabilizable subsystems is no less than a specified constant.3.The robust H_∞control of a class of switched cascade nonlinear systems is studied.The single Lyapunov function and multiple Lyapunov function approaches are utilized to construct composite Lyapunov functions,state feedback controllers and hysteresis or max/min switching strategies based on the special triangular form. Sufficient conditions for the solvability of robust H_∞control problem are developed.4.Robust H_∞control is investigated for a class of switched affine nonlinear systems with neutral uncertainties,which describes many practical parameter perturbations nonlinearly dependent on the state and state derivative.The multiple Lyapunov function and the common Lyapunov function approaches are exploited respectively for the cases that states are measurable or not.Correspondingly sufficient conditions are achieved via designing the state and output feedback controllers.5.The constructive H_∞control problems are solvable for two classes of switched affine nonlinear systems.First,the multiple Lyapunov function and the common Lyapunov function approaches are exploited for the cases where states are measurable or not,respectively.Correspondingly sufficient conditions with the state or output controllers guarantee the solvability of the robust H_∞control problems. Based on the explicit construction of Lyapunov functions,the results do not rely on positive definite solutions of the Hamilton-Jacobi(HJ) inequalities.Secondly, sufficient condition is derived for robust non-fragile H_∞control problem via the multiple Lyapunov function technique.Based on the construction of controllers,the results avoid solving the HJ inequalities.Finally,the results of the dissertation are summarized and further research topics are pointed out.