Stability and £ 2 gain analysis for discrete - Time LTI systems with controller failures

研究成果: Conference article

抄録

In this paper, we analyze stability and £ 2 gain properties for discrete-time linear time-invariant (LTI) systems controlled by a pre-designed dynamical output feedback controller which fails from time to time due to physical or purposeful reason. Our aim is to find conditions concerning controller failure time, under which the system's stability and £ 2 gain properties are preserved to a desired level. For stability, by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant and the average time interval between controller failures (ATBCF) is large enough, then global exponential stability of the system is guaranteed. For £ 2 gain, also by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant, then the system with an ATBCF achieves a reasonable weighted £ 2 gain level, and the weighted £2 gain approaches normal £ 2 gain when the ATBCF is sufficiently large.

元の言語English
ページ(範囲)545-550
ページ数6
ジャーナルIFAC Proceedings Volumes (IFAC-PapersOnline)
37
発行部数11
DOI
出版物ステータスPublished - 2004 1 1
イベント10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, LSS 2004 - Osaka, Japan
継続期間: 2004 7 262004 7 28

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Controllers
Lyapunov functions
Asymptotic stability
System stability
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ASJC Scopus subject areas

  • Control and Systems Engineering

これを引用

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title = "Stability and £ 2 gain analysis for discrete - Time LTI systems with controller failures",
abstract = "In this paper, we analyze stability and £ 2 gain properties for discrete-time linear time-invariant (LTI) systems controlled by a pre-designed dynamical output feedback controller which fails from time to time due to physical or purposeful reason. Our aim is to find conditions concerning controller failure time, under which the system's stability and £ 2 gain properties are preserved to a desired level. For stability, by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant and the average time interval between controller failures (ATBCF) is large enough, then global exponential stability of the system is guaranteed. For £ 2 gain, also by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant, then the system with an ATBCF achieves a reasonable weighted £ 2 gain level, and the weighted £2 gain approaches normal £ 2 gain when the ATBCF is sufficiently large.",
keywords = "(weighted) £ gain, Average time interval between controller failures (ATBCF), Dynamical output feedback, Exponential stability, Linear time-invariant (LTI) system, Piecewise Lyapunov function, Unavailability rate",
author = "Guisheng Zhai and Xinkai Chen and Hai Lin",
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T1 - Stability and £ 2 gain analysis for discrete - Time LTI systems with controller failures

AU - Zhai, Guisheng

AU - Chen, Xinkai

AU - Lin, Hai

PY - 2004/1/1

Y1 - 2004/1/1

N2 - In this paper, we analyze stability and £ 2 gain properties for discrete-time linear time-invariant (LTI) systems controlled by a pre-designed dynamical output feedback controller which fails from time to time due to physical or purposeful reason. Our aim is to find conditions concerning controller failure time, under which the system's stability and £ 2 gain properties are preserved to a desired level. For stability, by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant and the average time interval between controller failures (ATBCF) is large enough, then global exponential stability of the system is guaranteed. For £ 2 gain, also by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant, then the system with an ATBCF achieves a reasonable weighted £ 2 gain level, and the weighted £2 gain approaches normal £ 2 gain when the ATBCF is sufficiently large.

AB - In this paper, we analyze stability and £ 2 gain properties for discrete-time linear time-invariant (LTI) systems controlled by a pre-designed dynamical output feedback controller which fails from time to time due to physical or purposeful reason. Our aim is to find conditions concerning controller failure time, under which the system's stability and £ 2 gain properties are preserved to a desired level. For stability, by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant and the average time interval between controller failures (ATBCF) is large enough, then global exponential stability of the system is guaranteed. For £ 2 gain, also by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant, then the system with an ATBCF achieves a reasonable weighted £ 2 gain level, and the weighted £2 gain approaches normal £ 2 gain when the ATBCF is sufficiently large.

KW - (weighted) £ gain

KW - Average time interval between controller failures (ATBCF)

KW - Dynamical output feedback

KW - Exponential stability

KW - Linear time-invariant (LTI) system

KW - Piecewise Lyapunov function

KW - Unavailability rate

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