Study On The Stabilization Problem Of Two Kinds Of Higher Order Nonlinear Systems

The first chapter of this paper introduce the development of a high order nonlinear stochastic system and the finite time stable.The second chapter of this paper is concerned with the improvement of finite-time stability theorem and its application in stabilizing a class of high-order nonlinear systems globally.The novel control strategy unifies the construction of Lyapunov functions,which are used to deal with high-order and low-order nonlinear growth rates separately in the existing results.Convergent time is shortened greatly without requiring large control effort,but it suffers long period from traditional finite-time stabilization scheme when initial state is far away from the origin.Finally,two simulation examples including a practical one are presented to illustrate the efficiency of the proposed strategy.The third chapter of this paper is concerned with the problem of state-feedback stabilization for a more general class of stochastic high-order nonlinear systems.Under some weaker assumptions,based on the backstepping design method and sign function technique,a smooth state-feedback controller is designed,which ensures that the closed-loop system has an almost surely unique solution on,the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability.Finally,a simulation example is presented to demonstrate the control scheme.