TY - JOUR
T1 - Stability and £2 gain analysis for discrete - Time LTI systems with controller failures
AU - Zhai, Guisheng
AU - Chen, Xinkai
AU - Lin, Hai
N1 - Publisher Copyright:
© 2004 IFAC.
PY - 2004
Y1 - 2004
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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U2 - 10.1016/S1474-6670(17)31666-X
DO - 10.1016/S1474-6670(17)31666-X
M3 - Conference article
AN - SCOPUS:85064469612
VL - 37
SP - 545
EP - 550
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
SN - 2405-8963
IS - 11
T2 - 10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, LSS 2004
Y2 - 26 July 2004 through 28 July 2004
ER -