A Piecewise Approach to Control for Nonlinear Systems

抄録

In this paper, we present a basic concept to design a Lyapunov function candidate and the stabilizing controllers of nonlinear discrete-time systems. First, we propose a stabilization algorithm for linear step-varying discrete-time system via piecewise Lyapunov functions based on a tracking trajectory control. The piecewise Lyapunov functions satisfying arbitrary trajectory control can be constructed. The design conditions are represented as LMI conditions. Therefore, the solutions can be solved efficiently. The algorithm is applied to nonlinear discrete-time systems. Finally, some illustrated examples are given to show the validity of the proposed method.