The Robust Stabilization And H_∞ Control Problem Of Nonlinear Systems

Robust stabilization and H_∞ control problem of nonlinear systems play an important role in the field of control engineering . At first, H_∞ control problems for homogeneous systems are studied in this paper,then the robust stabilization of nonlinear discrete switched systems have been explored and robust stabilization of non-linear discrete-time systems with uncertain parameters are studied.Furthermore ,the problem of H_∞ control for symmetric Systems with time-delay via asynchronous controller switching is studied .Finally,we study the robust and adaptive control of H_∞ almost disturbance decoupling problem with stability for uncertain nonlinear systems. The main contributions of this paper are as following:In chapter 1. the basic conception and development results of nonlinear system are introduced,In chapter 2, firstly,the H_∞ control problems of time-delay nonlinear systems with homogeneous is discussed. Secondly ,the singular H_∞, of nonlinear systems with homogeneous properties is solved , the singular inputs of nonlinear time-delay system is decomposed into two parts:regular part input and singular part input. Then ,by vitue of Hamilton-Jacobi-Isaacs equations or inequalities , the regular nonlinear system H_∞ control problem is solved.Finally, the H_∞ Lyapunov function and the state feedback controller of the singular time-delay nonlinear systems with homogeneous properties are constructed.In chapter 3, the nonlinear singular stabilization and H_∞ control problem of systems with ordinary homogeneous properties is considered, the stabilization problems of nonlinear systems with homogeneous is discussed, by decomposition of the singular inputs of nonlinear homogeneous system into two parts:regular part input and singular part input ,and by vitue of Hamilton-Jacobi-Isaacs equations or inequalities ,the singular nonlinear system H_∞ control problem is solved and the Lyapunov function and the state feedback controller of the singular nonlinear systems withhomogeneous properties are constructed.In chapter 4, using switched Lyapunov function ,we studied the robust stabilization problem of switched systems with non-linear perturbations,and futhermore the robust stabilization problems of switched systems with time-delay and singular switched systems are discussed by LMI tools.In chapter 5, we deals with the problem of robust stabilization of non-linear discrete-time systems with uncertain parameters. The parameter uncertainties are assumed to be time-invariant and norm-bounded. Through a strict linear matrix inequality (LMI). sufficient conditions of exesitence of a memoryless state feedback controller which guarantees the stability of the closed-loop systems is given. By the end, we extend the result to discrete; time-delay systems.In chapter 6,The problem of U^ control for symmetric Systems with time-delay is discussed via asynchronous controller switching.Using the assumptions that a set of matrixes is strictly complete and matrix inequality , a asynchronous switched rule is constructed to ensure that Systems with time-delay have L2 gain,such that Hoc control problem for symmetric Systems with time-delay is solvedIn chapter 7,the robust and adaptive control of H^ almost disturbance decoupling problem with stability for uncertain nonlinear systems, which are of cascaded-like structure, is defined and investigated.Using Back-stepping method as a basic design tool, we show how to explicitly construct, in a recursive manner, a smooth adaptive controller, which ensures that the influence from the disturbance to the controlled output can be arbitrarily small, and the internal system is asymptotically stable.