A Novel Approach to Ensure Robust Stability using Unsymmetric Lyapunov Matrix for 2-D Discrete Model

Abstract

This paper addresses the issue of ensuring the asymptotic stability of the two-dimensional discrete Roesser model. Most of the emphasis is given now a days on the stability analysis of two-dimensional discrete models because of their wide variety of real time applications. When it comes of ensuring the stability of any system, the most generalized method is to use symmetric Lyapunov function. There have been a lot of published articles in which the stability of the system has been ensured using the symmetrical Lyapunov function, but use of unsymmetrical Lyapunov function has not been adopted due to the computational complexity. One of the very popular two dimensional discrete model is the Roesser model, which is structurally different from other two dimensional discrete models and has its wide applications in the field of image processing. In this article the stability of a 2-D discrete Roesser model has been ensured using the unsymmetrical Lyapunov function, which is a more generalized way of ensuring the stability of any system. Accordingly, new stability conditions have been developed, which is an extension of the previously reported methods in which the stability is made certain using the symmetrical Lyapunov matrix. In some cases, it has been shown numerically that it is difficult to ensure stability using the symmetric Lyapunov matrix but still, the stability for such cases may be ensured using the unsymmetric Lyapunov matrix. In addition, symmetrical Lyapunov matrix stability conditions have also been derived using the unsymmetric Lyapunov matrix. The stability criteria have been checked and ensured based on newly developed stability conditions by considering two different examples. An effort has been put in reducing the conservatism with the new stability conditions.