Relations between Common Lyapunov Functions of Quadratic and Infinity-Norm Forms for a Set of Discrete-Time LTI Systems

Thang Viet NGUYEN; Takehiro MORI; Yoshihiro MORI

doi:10.1093/ietfec/e89-a.6.1794

Relations between Common Lyapunov Functions of Quadratic and Infinity-Norm Forms for a Set of Discrete-Time LTI Systems

Thang Viet NGUYEN, Takehiro MORI, Yoshihiro MORI

Full Text Views

0

Share
Cite this

Summary :

This paper studies the problem of the relations between existence conditions of common quadratic and those of common infinity-norm Lyapunov functions for sets of discrete-time linear time-invariant (LTI) systems. Based on the equivalence between the robust stability of a class of time-varying systems and the existence of a common infinity-norm Lyapunov function for the corresponding set of LTI systems, the relations are determined. It turns out that although the relation is an equivalent one for single stable systems, the existence condition of common infinity-norm type is strictly implied by that of common quadratic type for the set of systems. Several existence conditions of a common infinity-norm Lyapunov functions are also presented for the purpose of easy checking.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.6 pp.1794-1798

Publication Date: 2006/06/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.6.1794

Type of Manuscript: PAPER

Category: Systems and Control

Cite this

Copy

Thang Viet NGUYEN, Takehiro MORI, Yoshihiro MORI, "Relations between Common Lyapunov Functions of Quadratic and Infinity-Norm Forms for a Set of Discrete-Time LTI Systems" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 6, pp. 1794-1798, June 2006, doi: 10.1093/ietfec/e89-a.6.1794.
Abstract: This paper studies the problem of the relations between existence conditions of common quadratic and those of common infinity-norm Lyapunov functions for sets of discrete-time linear time-invariant (LTI) systems. Based on the equivalence between the robust stability of a class of time-varying systems and the existence of a common infinity-norm Lyapunov function for the corresponding set of LTI systems, the relations are determined. It turns out that although the relation is an equivalent one for single stable systems, the existence condition of common infinity-norm type is strictly implied by that of common quadratic type for the set of systems. Several existence conditions of a common infinity-norm Lyapunov functions are also presented for the purpose of easy checking.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.6.1794/_p

Copy

@ARTICLE{e89-a_6_1794,
author={Thang Viet NGUYEN, Takehiro MORI, Yoshihiro MORI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Relations between Common Lyapunov Functions of Quadratic and Infinity-Norm Forms for a Set of Discrete-Time LTI Systems},
year={2006},
volume={E89-A},
number={6},
pages={1794-1798},
abstract={This paper studies the problem of the relations between existence conditions of common quadratic and those of common infinity-norm Lyapunov functions for sets of discrete-time linear time-invariant (LTI) systems. Based on the equivalence between the robust stability of a class of time-varying systems and the existence of a common infinity-norm Lyapunov function for the corresponding set of LTI systems, the relations are determined. It turns out that although the relation is an equivalent one for single stable systems, the existence condition of common infinity-norm type is strictly implied by that of common quadratic type for the set of systems. Several existence conditions of a common infinity-norm Lyapunov functions are also presented for the purpose of easy checking.},
keywords={},
doi={10.1093/ietfec/e89-a.6.1794},
ISSN={1745-1337},
month={June},}

Copy

TY - JOUR
TI - Relations between Common Lyapunov Functions of Quadratic and Infinity-Norm Forms for a Set of Discrete-Time LTI Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1794
EP - 1798
AU - Thang Viet NGUYEN
AU - Takehiro MORI
AU - Yoshihiro MORI
PY - 2006
DO - 10.1093/ietfec/e89-a.6.1794
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2006
AB - This paper studies the problem of the relations between existence conditions of common quadratic and those of common infinity-norm Lyapunov functions for sets of discrete-time linear time-invariant (LTI) systems. Based on the equivalence between the robust stability of a class of time-varying systems and the existence of a common infinity-norm Lyapunov function for the corresponding set of LTI systems, the relations are determined. It turns out that although the relation is an equivalent one for single stable systems, the existence condition of common infinity-norm type is strictly implied by that of common quadratic type for the set of systems. Several existence conditions of a common infinity-norm Lyapunov functions are also presented for the purpose of easy checking.
ER -