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Mastorakis, N.E., Mladenov, V.M. and Swamy, M.N.S. (2008) Neural Networks for Checking the Stability of Multidimensionalsystems. IEEE Symposium on Neural Network Applications in Electrical Engineering, Belgrade, 25-27 September 2008, 89-94.

has been cited by the following article:

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

  AUTHORS: P. Ramesh

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

  JOURNAL NAME: Circuits and Systems, Vol.7 No.6, May 12, 2016

  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 equivalentone- dimensional characteristic equation. Further formation of stability in the left of the z-plane, the roots of the characteristic equationf(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.