A Determinant Criterion for Stability Analysis and Design of Linear Discrete Systems

Original scientific paper Linear time invariant discrete systems can be described by constant coefficient linear difference equations. These equations can be easily transformed into the function of the complex variable by the z transform method. Two triangular matrices are formed with the help of the coefficients of system characteristics equation along with the minimal shifting of coefficients either left or right and elimination of coefficient method. A single square matrix is constructed by adding the two triangular matrices. The proposed method of construction of square matrix consumes less arithmetic operations like shifting and eliminating of coefficients, when compared to the construction of Square matrix by Jury’s and Hurwitz matrix method. This Square matrix is used for testing the sufficient condition utilising Jury’s Inner determinant procedure. Further one more necessary condition is also suggested along with Jury’s conditions for stability. Illustrations are also included to show the applicability of the proposed scheme. Also an algorithm was developed for finding the design parameter k-value which helps to design a stable Linear Time Invariant Discrete System.