A parameter-dependent Lyapunov function based design approach for gain-scheduled Hâˆž filters of LPV systems

Shaosheng Zhou; Baoyong Zhang; Wei Xing Zheng; David Castanon; James C. Spall

A parameter-dependent Lyapunov function based design approach for gain-scheduled Hâˆž filters of LPV systems

Shaosheng Zhou, Baoyong Zhang, Wei Xing Zheng, David Castanon, James C. Spall

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

Abstract

In this paper we study the problem of designing gain-scheduled Hâˆž filters for a class of parameter-varying discrete-time systems. We utilize a parameter-dependent Lyapunov function to establish a new characterization of asymptotic stability with Hâˆž norm bound for the linear parameter-varying (LPV) systems. On the basis of the stability with Hâˆž performance characterization established, we provide sufficient conditions for the solvability of the filter design problem by means of a finite number of linear matrix inequalities (LMIs). Then we show that solving a set of LMIs paves the way for designing a desired gain-scheduled Hâˆž filter. We also use a numerical example to demonstrate the application of the presented filter design method.

Original language	English
Title of host publication	46th IEEE Conference on Decision and Control : December 12-14, 2007, New Orleans, LA, USA
Publisher	IEEE
Number of pages	6
ISBN (Print)	1424414989
Publication status	Published - 2007
Event	IEEE Conference on Decision and Control - Duration: 12 Dec 2017 → …

Conference

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

Keywords

H∞ control
linear matrix inequalities
linear control systems
Lyapunov functions
filters (mathematics)
time delay systems

Cite this

@inproceedings{a8d1890aa81e4937a8de54e416b7bd77,

title = "A parameter-dependent Lyapunov function based design approach for gain-scheduled H{\^a}ˆ{\v z} filters of LPV systems",

abstract = "In this paper we study the problem of designing gain-scheduled H{\^a}ˆ{\v z} filters for a class of parameter-varying discrete-time systems. We utilize a parameter-dependent Lyapunov function to establish a new characterization of asymptotic stability with H{\^a}ˆ{\v z} norm bound for the linear parameter-varying (LPV) systems. On the basis of the stability with H{\^a}ˆ{\v z} performance characterization established, we provide sufficient conditions for the solvability of the filter design problem by means of a finite number of linear matrix inequalities (LMIs). Then we show that solving a set of LMIs paves the way for designing a desired gain-scheduled H{\^a}ˆ{\v z} filter. We also use a numerical example to demonstrate the application of the presented filter design method.",

keywords = "H∞ control, linear matrix inequalities, linear control systems, Lyapunov functions, filters (mathematics), time delay systems",

author = "Shaosheng Zhou and Baoyong Zhang and Zheng, {Wei Xing} and David Castanon and Spall, {James C.}",

year = "2007",

language = "English",

isbn = "1424414989",

booktitle = "46th IEEE Conference on Decision and Control : December 12-14, 2007, New Orleans, LA, USA",

publisher = "IEEE",

note = "IEEE Conference on Decision and Control ; Conference date: 12-12-2017",

}

TY - GEN

T1 - A parameter-dependent Lyapunov function based design approach for gain-scheduled Hâˆž filters of LPV systems

AU - Zhou, Shaosheng

AU - Zhang, Baoyong

AU - Zheng, Wei Xing

AU - Castanon, David

AU - Spall, James C.

PY - 2007

Y1 - 2007

N2 - In this paper we study the problem of designing gain-scheduled Hâˆž filters for a class of parameter-varying discrete-time systems. We utilize a parameter-dependent Lyapunov function to establish a new characterization of asymptotic stability with Hâˆž norm bound for the linear parameter-varying (LPV) systems. On the basis of the stability with Hâˆž performance characterization established, we provide sufficient conditions for the solvability of the filter design problem by means of a finite number of linear matrix inequalities (LMIs). Then we show that solving a set of LMIs paves the way for designing a desired gain-scheduled Hâˆž filter. We also use a numerical example to demonstrate the application of the presented filter design method.

AB - In this paper we study the problem of designing gain-scheduled Hâˆž filters for a class of parameter-varying discrete-time systems. We utilize a parameter-dependent Lyapunov function to establish a new characterization of asymptotic stability with Hâˆž norm bound for the linear parameter-varying (LPV) systems. On the basis of the stability with Hâˆž performance characterization established, we provide sufficient conditions for the solvability of the filter design problem by means of a finite number of linear matrix inequalities (LMIs). Then we show that solving a set of LMIs paves the way for designing a desired gain-scheduled Hâˆž filter. We also use a numerical example to demonstrate the application of the presented filter design method.

KW - H∞ control

KW - linear matrix inequalities

KW - linear control systems

KW - Lyapunov functions

KW - filters (mathematics)

KW - time delay systems

UR - http://handle.uws.edu.au:8081/1959.7/45155

M3 - Conference Paper

SN - 1424414989

BT - 46th IEEE Conference on Decision and Control : December 12-14, 2007, New Orleans, LA, USA

PB - IEEE

T2 - IEEE Conference on Decision and Control

Y2 - 12 December 2017

ER -

A parameter-dependent Lyapunov function based design approach for gain-scheduled Hâˆž filters of LPV systems

Abstract

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Keywords

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