A Modified Stability Analysis of Two-Dimensional Linear Time Invariant Discrete Systems within the Unity-Shifted Unit Circle

Periyasamy Ramesh

doi:10.4236/cs.2016.73011

Abstract

This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.

Highlights

In the last decades a vast amount of research was devoted to the area of two-dimensional systems
The stability test is carried out by the new stability test theorem we presented in frequency domain which has the limitation of Jury’s and can be used in both conditions of linear and non-linear systems
Further Jury 1971 had presented the positive inner wise and positive definite symmetric matrices for stability of the system. In this method the formulations of symmetric matrices were very complicated and this criterion was rarely used by engineers for high order system. In this present paper a simple and direct scheme is proposed to find stability of linear time invariant discrete systems compared to the Jury (1971) method

Summary

Introduction

In the last decades a vast amount of research was devoted to the area of two-dimensional systems. From the control view point stability analysis of a 2-D model is of interest, since a variety of distributed systems, such as time-delay systems, linear multi pass processes and systems governed by certain types of partial differential equations, fit quite naturally in the framework of 2-D system theory All these initial studies of the stability were carried in frequency domain (Z domain). In this method the formulations of symmetric matrices were very complicated and this criterion was rarely used by engineers for high order system In this present paper a simple and direct scheme is proposed to find stability of linear time invariant discrete systems compared to the Jury (1971) method. One more necessary condition is proposed along with Jury’s condition for stability

Literature Survey

Proposed Method

Illustrations

Z12 Z 2

Result and Discussion

Conclusion