非线性离散系统基于控制Lyapunov函数的反馈镇定

Feedback Stabilization of Discrete-Time Nonlinear Systems on the Basis of Control Lyapunov Function

以控制Lyapunov函数为基础,研究了一类具有多个输入的非线性时间离散系统的反馈镇定问题.在假设存在一个二次型控制Lyapunov函数的前提下,明确给出了使得这类系统的零解全局渐近稳定的反馈控制律.根据LaSalle不变性原理,建立了使得闭环系统稳定的充分条件.这一结论推广和改进了具有单个输入的仿射非线性系统的反馈镇定问题.

By employing the control Lyapunov function,a class of discrete-time nonlinear systems with multiple inputs was researched. Under the assumption that there exists a quadratic control Lyapunov function, a feedback control law was provided explicitly which renders the origin of this class of systems globally asymptotically stable.Applying the LaSalle invariance principle, a sufficient condition for stabilizing the closed-loop systems was established. This result is generalization and improvement of the feedback stabilization for single-input discrete-time systems affine in the control.