Robust stabilization of uncertain time delay systems via internal and external approaches

Akira Kojima; Kenko Uchida; Etsujiro Shimemura

Robust stabilization of uncertain time delay systems via internal and external approaches

Akira Kojima^*, Kenko Uchida, Etsujiro Shimemura

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The authors solve a robust stabilization problem defined for time delay systems. They take a twofold approach to the derivation of the robust stabilizing control law: the internal approach based on a Lyapunov type operator equation and the external approach based on the small-gain theorem. The internal approach enables one to solve a restricted robust stabilization problem by introducing an indefinite Riccati type operator equation. Then, as the internal approach is not applicable for the analysis of the point delay element, the external approach is used to analyze the robust stability against the uncertainty of the point delay element. Finally, by exploiting the merits of both approaches, a robust stabilizing control law against all types of the perturbations is obtained.

Original language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Publisher	Publ by IEEE
Pages	1624-1626
Number of pages	3
Volume	3
Publication status	Published - 1990
Event	Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA Duration: 1990 Dec 5 → 1990 Dec 7

Other

Other	Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6)
City	Honolulu, HI, USA
Period	90/12/5 → 90/12/7

ASJC Scopus subject areas

Chemical Health and Safety
Control and Systems Engineering
Safety, Risk, Reliability and Quality

Cite this

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title = "Robust stabilization of uncertain time delay systems via internal and external approaches",

abstract = "The authors solve a robust stabilization problem defined for time delay systems. They take a twofold approach to the derivation of the robust stabilizing control law: the internal approach based on a Lyapunov type operator equation and the external approach based on the small-gain theorem. The internal approach enables one to solve a restricted robust stabilization problem by introducing an indefinite Riccati type operator equation. Then, as the internal approach is not applicable for the analysis of the point delay element, the external approach is used to analyze the robust stability against the uncertainty of the point delay element. Finally, by exploiting the merits of both approaches, a robust stabilizing control law against all types of the perturbations is obtained.",

author = "Akira Kojima and Kenko Uchida and Etsujiro Shimemura",

year = "1990",

language = "English",

volume = "3",

pages = "1624--1626",

booktitle = "Proceedings of the IEEE Conference on Decision and Control",

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note = "Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) ; Conference date: 05-12-1990 Through 07-12-1990",

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T1 - Robust stabilization of uncertain time delay systems via internal and external approaches

AU - Kojima, Akira

AU - Uchida, Kenko

AU - Shimemura, Etsujiro

PY - 1990

Y1 - 1990

N2 - The authors solve a robust stabilization problem defined for time delay systems. They take a twofold approach to the derivation of the robust stabilizing control law: the internal approach based on a Lyapunov type operator equation and the external approach based on the small-gain theorem. The internal approach enables one to solve a restricted robust stabilization problem by introducing an indefinite Riccati type operator equation. Then, as the internal approach is not applicable for the analysis of the point delay element, the external approach is used to analyze the robust stability against the uncertainty of the point delay element. Finally, by exploiting the merits of both approaches, a robust stabilizing control law against all types of the perturbations is obtained.

AB - The authors solve a robust stabilization problem defined for time delay systems. They take a twofold approach to the derivation of the robust stabilizing control law: the internal approach based on a Lyapunov type operator equation and the external approach based on the small-gain theorem. The internal approach enables one to solve a restricted robust stabilization problem by introducing an indefinite Riccati type operator equation. Then, as the internal approach is not applicable for the analysis of the point delay element, the external approach is used to analyze the robust stability against the uncertainty of the point delay element. Finally, by exploiting the merits of both approaches, a robust stabilizing control law against all types of the perturbations is obtained.

UR - http://www.scopus.com/inward/record.url?scp=0025559780&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:0025559780

VL - 3

SP - 1624

EP - 1626

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

T2 - Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6)

Y2 - 5 December 1990 through 7 December 1990

ER -

Robust stabilization of uncertain time delay systems via internal and external approaches

Abstract

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ASJC Scopus subject areas

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