Stability Analysis of 2D Discrete Linear System Described by the Fornasini-Marchesini Second Model with Actuator Saturation

Richa Negi,Haranath Kar,Shubhi Purwar

doi:10.5402/2012/847178

Abstract

This paper proposes a novel antiwindup controller for 2D discrete linear systems with saturating controls in Fornasini-Marchesini second local state space (FMSLSS) setting. A Lyapunov-based method to design an antiwindup gain of 2D discrete systems with saturating controls is established. Stability conditions allowing the design of antiwindup loops, in both local and global contexts have been derived. Numerical examples are provided to illustrate the applicability of the proposed method.

Highlights

An important problem which is always inherent to all dynamical systems is the presence of actuator saturation nonlinearities
Inspired by the results [9] for 1D discrete-time systems, this paper investigates the antiwindup problem for 2D discrete systems described by Fornasini-Marchesini second local state space (FMSLSS) model with saturating controls
A Lyapunov-based approach to design an antiwindup gain of 2D discrete systems with saturating controls in the FMSLSS setting is established

Summary

Introduction

An important problem which is always inherent to all dynamical systems is the presence of actuator saturation nonlinearities. The stability analysis of the continuous as well as discrete time linear systems with saturating controls has been widely considered for one-dimensional (1D) systems [1,2,3,4,5,6,7,8,9,10]. Inspired by the results [9] for 1D discrete-time systems, this paper investigates the antiwindup problem for 2D discrete systems described by FMSLSS model with saturating controls. The paper aims at providing a technique to compute the antiwindup gain of the 2D dynamic compensator that ensures the stability of the overall closed loop system in local as well as global context.

Problem Statement

Main Results

Numerical Examples

Conclusions