Nonlinear Tracking Control via Piecewise Lyapunov Functions

Abstract

This paper presents a concept to design a Lyapunov function candidate and the stabilizing controllers of nonlinear discrete-time systems. A stabilization algorithm for linear step-varying discrete-time system is proposed via piecewise Lyapunov functions based on a tracking trajectory control. This tracking control can be applied to arbitrary trajectories. The solutions can be solved efficiently because the design conditions are represented as linear matrix inequality (LMI) conditions. We apply the algorithm to nonlinear discrete-time systems. An illustrated example is given to show the validity of the proposed method.