Stability Analysis of Multi-Dimensional Linear Time Invariant Discrete Systems within the Unity Shifted Unit Circle ()
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.
Share and Cite:
Ramesh, P. (2016) Stability Analysis of Multi-Dimensional Linear Time Invariant Discrete Systems within the Unity Shifted Unit Circle.
Circuits and Systems,
7, 709-717. doi:
10.4236/cs.2016.76060.