Quadratic stabilizability and H∞ disturbance attenuation of switched linear systems via state and output feedback

Guisheng Zhai

doi:10.1109/CDC.2012.6426876

Quadratic stabilizability and H_∞ disturbance attenuation of switched linear systems via state and output feedback

Guisheng Zhai

Research output: Contribution to journal › Conference article › peer-review

10 Citations (Scopus)

Abstract

We consider quadratic stabilizability and H_∞ disturbance attenuation of switched systems which are composed of a finite set of linear time-invariant subsystems. The situation is that none of the subsystems is quadratically stable with certain H_∞ disturbance attenuation level but a convex combination of the subsystems achieves such performance. We then design a state-dependent switching signal (state feedback) and an output-dependent switching signal (output feedback) such that the entire switched system is quadratically stable with the same H_∞ disturbance attenuation level. In the case of state feedback, when the number of subsystems is two, we show that the existence of desired convex combination of subsystems is not only sufficient but also necessary for quadratic stabilizability with the H_∞ disturbance attenuation of the switched system.

Original language	English
Article number	6426876
Pages (from-to)	1935-1940
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/CDC.2012.6426876
Publication status	Published - 2012
Event	51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: 2012 Dec 10 → 2012 Dec 13

Keywords

LMI
Switched linear systems
convex combination
matrix inequalities
output feedback
quadratic stabilizability
state feedback

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2012.6426876

Cite this

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title = "Quadratic stabilizability and H∞ disturbance attenuation of switched linear systems via state and output feedback",

abstract = "We consider quadratic stabilizability and H∞ disturbance attenuation of switched systems which are composed of a finite set of linear time-invariant subsystems. The situation is that none of the subsystems is quadratically stable with certain H∞ disturbance attenuation level but a convex combination of the subsystems achieves such performance. We then design a state-dependent switching signal (state feedback) and an output-dependent switching signal (output feedback) such that the entire switched system is quadratically stable with the same H∞ disturbance attenuation level. In the case of state feedback, when the number of subsystems is two, we show that the existence of desired convex combination of subsystems is not only sufficient but also necessary for quadratic stabilizability with the H∞ disturbance attenuation of the switched system.",

keywords = "LMI, Switched linear systems, convex combination, matrix inequalities, output feedback, quadratic stabilizability, state feedback",

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language = "English",

pages = "1935--1940",

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

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note = "51st IEEE Conference on Decision and Control, CDC 2012 ; Conference date: 10-12-2012 Through 13-12-2012",

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AU - Zhai, Guisheng

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N2 - We consider quadratic stabilizability and H∞ disturbance attenuation of switched systems which are composed of a finite set of linear time-invariant subsystems. The situation is that none of the subsystems is quadratically stable with certain H∞ disturbance attenuation level but a convex combination of the subsystems achieves such performance. We then design a state-dependent switching signal (state feedback) and an output-dependent switching signal (output feedback) such that the entire switched system is quadratically stable with the same H∞ disturbance attenuation level. In the case of state feedback, when the number of subsystems is two, we show that the existence of desired convex combination of subsystems is not only sufficient but also necessary for quadratic stabilizability with the H∞ disturbance attenuation of the switched system.

AB - We consider quadratic stabilizability and H∞ disturbance attenuation of switched systems which are composed of a finite set of linear time-invariant subsystems. The situation is that none of the subsystems is quadratically stable with certain H∞ disturbance attenuation level but a convex combination of the subsystems achieves such performance. We then design a state-dependent switching signal (state feedback) and an output-dependent switching signal (output feedback) such that the entire switched system is quadratically stable with the same H∞ disturbance attenuation level. In the case of state feedback, when the number of subsystems is two, we show that the existence of desired convex combination of subsystems is not only sufficient but also necessary for quadratic stabilizability with the H∞ disturbance attenuation of the switched system.

KW - LMI

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KW - convex combination

KW - matrix inequalities

KW - output feedback

KW - quadratic stabilizability

KW - state feedback

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