Applied Lyapunov Stability on Output Tracking Problem for a Class of Discrete-Time Linear Systems

TL;DR

This paper presents a simple Lyapunov-based method for designing robust output tracking controllers for discrete-time linear systems, ensuring convergence of tracking error with easy implementation.

Contribution

It introduces a Lyapunov equation-based approach for robust tracking control using linear controllers, simplifying design and implementation for perturbed systems.

Findings

Convergence of tracking error to zero is proven.

Method is applicable to perturbed systems.

Numerical examples validate the approach.

Abstract

The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a reference model. By using the solution of the Lyapunov equation, the convergence of the tracking error to the origin, is proved. The proposed approach employs linear controllers rather than nonlinear ones. Therefore, the designing method is simple for use and the resulting controller is easy to implement. An application of the proposed approach for a class of perturbed systems is also considered. Finally, numerical examples are given to demonstrate the validity of the results.