Title :
Stability and the Lyapunov equation for n-dimensional digital systems
Author :
Xiao, Chengshan ; Hill, David J. ; Agathoklis, Pan
Author_Institution :
Dept. of Electr. Eng., Sydney Univ., NSW, Australia
fDate :
7/1/1997 12:00:00 AM
Abstract :
The discrete-time bounded-real lemma for nonminimal discrete systems is presented. Based on this lemma, rigorous necessary and sufficient conditions for the existence of positive definite solutions to the Lyapunov equation for n-dimensional (n-D) digital systems are proposed. These new conditions can be applied to n-D digital systems with n-D characteristic polynomials involving factor polynomials of any dimension, 1-D to n-D. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of an n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (0⩽k⩽n) subsystem and m (1⩽m⩽n) 1-D subsystems. This could significantly simplify the complexity of solving the n-D Lyapunov equation for such cases
Keywords :
Lyapunov methods; circuit stability; discrete time filters; polynomials; two-dimensional digital filters; Lyapunov equation; characteristic polynomials; discrete-time bounded-real lemma; factor polynomials; n-dimensional digital systems; nonminimal discrete systems; positive definite solutions; stability; subsystems; Australia; Digital systems; Equations; Multidimensional systems; Observability; Polynomials; Stability analysis; Sufficient conditions;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on