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

P. Ramesh

Department of Electrical and Electronics Engineering, Anna University, University College of Engineering, Ramanathapuram, India.

DOI: 10.4236/cs.2016.76060                

Abstract

This technical brief proposes a new approach to multi-dimensional linear time invariant discrete systems within the unity shifted unit circle which is denoted in the form of characteristic equation. The characteristic equation of multi–dimensional linear system is modified into an equivalent one- dimensional characteristic equation. Further formation of stability in the left of the z-plane, the roots of the characteristic equation f(z) =0 should lie within the shifted unit circle. Using the coefficients of the unity shifted one dimensional equivalent characteristic equation by applying minimal shifting of coefficients either left or right and elimination of coefficient method to two triangular matrixes are formed. A single square matrix is formed by adding the two triangular matrices. This matrix is used for testing the sufficient condition by proposed Jury’s inner determinant concept. Further one more indispensable condition is suggested to show the applicability of the proposed scheme. The proposed method of construction of square matrix consumes less arithmetic operation like shifting and eliminating of coefficients when compare to the construction of square matrix by Jury’s and Hurwitz matrix method.

Keywords

Stability, Multi-Dimensional, Unity-Shifting, Characteristics Equations, Inner Determinants

Conflicts of Interest

The authors declare no conflicts of interest.

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