This paper derives conditions for the stability of discrete-time systems that can be modeled by a vector difference equation, where the variables are m x 1 vectors and the coefficients are m x m matrices. Stability of the system is related to the locations of the roots of the determinant of a real m x m matrix polynomial of nth order. In this case, sufficient conditions for the system to be stable are derived. The conditions are imposed on the infinity norm of two matrices constructed from the coefficient matrices and do not require the computation of the determinant polynomial. The conditions are the extensions of one of the Jury sufficient conditions for a scalar polynomial. An example is used to illustrate the application of the sufficient conditions
K. T. Ngo and K. T. Erickson, "Stability of Discrete-Time Matrix Polynomials," IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers (IEEE), Jan 1997.
The definitive version is available at https://doi.org/10.1109/9.566665
Electrical and Computer Engineering
Keywords and Phrases
Jury Sufficient Conditions; Coefficient Matrices; Difference Equations; Discrete Time Systems; Discrete-Time Matrix Polynomials; Discrete-Time Systems; Linear Systems; M Matrices; M X 1 Vectors; M X M; Polynomial Matrices; Scalar Polynomial; Stability; Sufficient Conditions; Vector Difference Equation; Vectors
International Standard Serial Number (ISSN)
Article - Journal
© 1997 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.