Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

Manish Tiwari,Amit Dhawan

doi:10.4236/jsip.2012.32034

Abstract

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

Highlights

In recent years, due to theoretical as well as application importance in the fields such as digital filtering, image processing, seismographic data processing, thermal processes, gas absorption, water stream heating etc. [1,2,3,4,5,6,7,8], the two-dimensional (2-D) systems have received considerable attention
New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees the asymptotic stability of closed loop systems, and an adequate performance bound over all the admissible parameter uncertainties
A convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function

Summary

Introduction

Due to theoretical as well as application importance in the fields such as digital filtering, image processing, seismographic data processing, thermal processes, gas absorption, water stream heating etc. [1,2,3,4,5,6,7,8], the two-dimensional (2-D) systems have received considerable attention. Sufficient conditions for the asymptotic stability of 2-D systems described by the FM first model have been presented in [11,12,13]. An improved Lyapunov based sufficient condition for the stability of 2-D linear systems described by the FM first model has been proposed in [14], and it is shown that the criterion given in [14] is less restrictive than those reported in [11,12]. In [20], necessary and sufficient conditions for the asymptotic stability of the FM first model using non-negative matrix theory have been proposed, and it has been shown that the conditions are sharper than those reported in [10,11,17]. A survey of the existing literature on the stability of the 2-D discrete systems described by FM first model has been presented in [21]

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