Stability and the Lyapunov equation for n-dimensional digital systems

Chengshan Xiao; David J. Hill; P. Agathoklis

Stability and the Lyapunov equation for n-dimensional digital systems

Chengshan Xiao
, David J. Hill
, P. Agathoklis

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

Abstract

The discrete-time bounded-real lemma is further developed for nonminimal digital systems. 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 are improvements and extensions of earlier conditions and can be applied to n-D digital systems with characteristic polynomials involving 1-D factor polynomials. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of a n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (o ≤ 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.

Original language	English
Title of host publication	IEEE International Symposium on Circuits and Systems
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	781-784
Number of pages	4
Volume	2
Publication status	Published - 1995
Externally published	Yes
Event	IEEE International Symposium on Circuits and Systems 1995 - Seattle, United States of America Duration: 30 Apr 1995 → 3 May 1995 https://ieeexplore.ieee.org/xpl/conhome/3941/proceeding (Proceedings)

Conference

Conference	IEEE International Symposium on Circuits and Systems 1995
Abbreviated title	ISCAS 1995
Country/Territory	United States of America
City	Seattle
Period	30/04/95 → 3/05/95
Internet address	https://ieeexplore.ieee.org/xpl/conhome/3941/proceeding (Proceedings)

Cite this

@inproceedings{b159b833ee224466954ea18a4d43065a,

title = "Stability and the Lyapunov equation for n-dimensional digital systems",

abstract = "The discrete-time bounded-real lemma is further developed for nonminimal digital systems. 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 are improvements and extensions of earlier conditions and can be applied to n-D digital systems with characteristic polynomials involving 1-D factor polynomials. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of a n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (o ≤ 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.",

author = "Chengshan Xiao and Hill, \{David J.\} and P. Agathoklis",

year = "1995",

language = "English",

volume = "2",

pages = "781--784",

booktitle = "IEEE International Symposium on Circuits and Systems",

publisher = "IEEE, Institute of Electrical and Electronics Engineers",

address = "United States of America",

note = "IEEE International Symposium on Circuits and Systems 1995, ISCAS 1995 ; Conference date: 30-04-1995 Through 03-05-1995",

url = "https://ieeexplore.ieee.org/xpl/conhome/3941/proceeding",

}

TY - GEN

T1 - Stability and the Lyapunov equation for n-dimensional digital systems

AU - Xiao, Chengshan

AU - Hill, David J.

AU - Agathoklis, P.

PY - 1995

Y1 - 1995

N2 - The discrete-time bounded-real lemma is further developed for nonminimal digital systems. 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 are improvements and extensions of earlier conditions and can be applied to n-D digital systems with characteristic polynomials involving 1-D factor polynomials. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of a n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (o ≤ 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.

AB - The discrete-time bounded-real lemma is further developed for nonminimal digital systems. 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 are improvements and extensions of earlier conditions and can be applied to n-D digital systems with characteristic polynomials involving 1-D factor polynomials. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of a n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (o ≤ 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.

UR - https://www.scopus.com/pages/publications/0029204173

M3 - Conference Paper

AN - SCOPUS:0029204173

VL - 2

SP - 781

EP - 784

BT - IEEE International Symposium on Circuits and Systems

PB - IEEE, Institute of Electrical and Electronics Engineers

T2 - IEEE International Symposium on Circuits and Systems 1995

Y2 - 30 April 1995 through 3 May 1995

ER -

Stability and the Lyapunov equation for n-dimensional digital systems

Abstract

Conference

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