A note on a double convex combination matrix inequality

Shaosheng Zhou; Wei Xing Zheng

A note on a double convex combination matrix inequality

Shaosheng Zhou
, Wei Xing Zheng

School of Computer, Data & Mathematical Sciences

Research output: Chapter in Book / Conference Paper › Conference Paper

Abstract

A double convex combination matrix inequality rising in control and filtering problems of dynamic systems is revisited in this paper. Focus is placed on comparisons of conservatism caused by some commonlyused sufficient conditions which ensure the validity of the double convex combination matrix inequality. It is found that the conservatism of analysis and synthesis results of the control and filtering problems for a large class of systems, such as polytopic systems, parameter varying systems as well as Takagi-Sugeno (TS) model based nonlinear systems, mainly involves the sufficient conditions corresponding to the double convex combination matrix inequality. Four sufficient conditions for the validity of the double convex combination matrix inequality are presented. By the matrix-string set approach and analytic tools of negative semi-definiteness of symmetric matrices, detailed comparison results for conservatism of these sufficient conditions are provided.

Original language	English
Title of host publication	Proceedings of the 49th IEEE Conference on Decision and Control, held in Atlanta, USA, 15-17 Dec. 2010
Publisher	IEEE Press
Pages	4287-4292
Number of pages	6
ISBN (Print)	9781424477456
Publication status	Published - 2010
Event	IEEE Conference on Decision and Control - Duration: 12 Dec 2017 → …

Conference

Conference	IEEE Conference on Decision and Control
Period	12/12/17 → …

Keywords

matrices
nonlinear control theory

Cite this

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title = "A note on a double convex combination matrix inequality",

abstract = "A double convex combination matrix inequality rising in control and filtering problems of dynamic systems is revisited in this paper. Focus is placed on comparisons of conservatism caused by some commonlyused sufficient conditions which ensure the validity of the double convex combination matrix inequality. It is found that the conservatism of analysis and synthesis results of the control and filtering problems for a large class of systems, such as polytopic systems, parameter varying systems as well as Takagi-Sugeno (TS) model based nonlinear systems, mainly involves the sufficient conditions corresponding to the double convex combination matrix inequality. Four sufficient conditions for the validity of the double convex combination matrix inequality are presented. By the matrix-string set approach and analytic tools of negative semi-definiteness of symmetric matrices, detailed comparison results for conservatism of these sufficient conditions are provided.",

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booktitle = "Proceedings of the 49th IEEE Conference on Decision and Control, held in Atlanta, USA, 15-17 Dec. 2010",

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TY - GEN

T1 - A note on a double convex combination matrix inequality

AU - Zhou, Shaosheng

AU - Zheng, Wei Xing

PY - 2010

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N2 - A double convex combination matrix inequality rising in control and filtering problems of dynamic systems is revisited in this paper. Focus is placed on comparisons of conservatism caused by some commonlyused sufficient conditions which ensure the validity of the double convex combination matrix inequality. It is found that the conservatism of analysis and synthesis results of the control and filtering problems for a large class of systems, such as polytopic systems, parameter varying systems as well as Takagi-Sugeno (TS) model based nonlinear systems, mainly involves the sufficient conditions corresponding to the double convex combination matrix inequality. Four sufficient conditions for the validity of the double convex combination matrix inequality are presented. By the matrix-string set approach and analytic tools of negative semi-definiteness of symmetric matrices, detailed comparison results for conservatism of these sufficient conditions are provided.

AB - A double convex combination matrix inequality rising in control and filtering problems of dynamic systems is revisited in this paper. Focus is placed on comparisons of conservatism caused by some commonlyused sufficient conditions which ensure the validity of the double convex combination matrix inequality. It is found that the conservatism of analysis and synthesis results of the control and filtering problems for a large class of systems, such as polytopic systems, parameter varying systems as well as Takagi-Sugeno (TS) model based nonlinear systems, mainly involves the sufficient conditions corresponding to the double convex combination matrix inequality. Four sufficient conditions for the validity of the double convex combination matrix inequality are presented. By the matrix-string set approach and analytic tools of negative semi-definiteness of symmetric matrices, detailed comparison results for conservatism of these sufficient conditions are provided.

KW - matrices

KW - nonlinear control theory

UR - http://handle.uws.edu.au:8081/1959.7/504727

M3 - Conference Paper

SN - 9781424477456

SP - 4287

EP - 4292

BT - Proceedings of the 49th IEEE Conference on Decision and Control, held in Atlanta, USA, 15-17 Dec. 2010

PB - IEEE Press

T2 - IEEE Conference on Decision and Control

Y2 - 12 December 2017

ER -

A note on a double convex combination matrix inequality

Abstract

Conference

Keywords

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