The Parameters Of Typical Nonlinear System Stability Analysis And Controller Design

The designs of nonlinear systems are the challenging topics in the control field and the focus of control theory research. Many industrial production systems not only have nonlinear characteristics, but also include a set of unknown parameters whose value cannot be predicted with any precision. The parameters change with the environment. In these tyes of nonlinear systems, the two improtant basic problem are the existence of moving equilibria and the analysis of stability, what’s more, it is related each other. Therefore it is necessary to synthetically analyse the parametric stability for the nonlinear system with parameters. The main contexts of this thesis show as follows:(1) The parametric absolute stabilization for Lurie time-delay systems with polytopic uncertainty is investigated. First, the existing condition of parametric stability and the stable region are studied by change of the uncertain parameters and reference input based on decentralized state feedback. Then, a delay-dependent parametric stability condition in the equilibrium existence region for Lurie time-delay systems with polytopic uncertainty is proposed through linear matrix inequality method. A numerical example is given to show the effectiveness of the proposed method.(2) When the uncertain parameters vary in a wide range, a single controller design method is usually difficult to guarantee stability of the nonlinear systems with parametric uncertainty. If the uncertain parameters are divided into several specific parameter subset and controllers are designed among each parameter subset, the controllers can switched according to the scope of parameters to expaned the parametric stability ranges of the nonlinear systems. The problem of parametric stabilization of nonlinear systems using switching control strategy is considered in this thesis. Firstly, the existences of moving equilibrium for nonlinear systems with parameters variations are analysed and the solution of nonlinear algebraic equations is involved. Then, using multiple Lyapunov function, a parametric stabilization condition for the nonlinear systems is formulated based on linear matrix inequality. Furthermore, appropriate switching rules are designed to be activated safely in the parametric stability region. The results show that this design of the switching controller enables the nonlinear systems stabilized in a wide range.(3) The parametric H∞control problem of nonlinear systems with uncertain parameters is investigated. Firstly, when input disturbance isn’t considered, the existence region of equilibrium involves the solution of nonlinear algebraic equations. Then, when the disturbance input exists, state feedback controllers are designed and the sufficient conditions which made the closed-loop system parametric stable and satisfied H∞index of performance are formulated by using Lyapunov function. The results show that the designed controllers can effectively stabilize the nonlinear systems and the nonlinear systems have certain H∞index of performance.