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International Journal of Control Volume 77, 2004 - Issue 1
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Original Articles

A unifying framework for the SISO circle criterion and other quadratic stability criteria

Robert N. Shorten Hamilton Institute, NUI Maynooth, Kildare, Ireland
,
Oliver Mason Hamilton Institute, NUI Maynooth, Kildare, Ireland
,
Fiacre O’Cairbre Mathematics Dept., NUI Maynooth, Kildare, Ireland
&
Paul Curran Department of Electrical Engineering, NUI Dublin, Dublin 4, Ireland
Pages 1-8 | Received 10 Dec 2002, Accepted 06 Oct 2003, Published online: 19 Feb 2007

References

References

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  • Kalman , R . 1963 . Lyapunov functions for the problem of Lur’e in automatic control . Proceedings of the National Academy of Sciences , 49 : 201 – 205 .
  • Laffey T Shorten R O’Cairbre F 2002 On the stability of convex sums of rank-1 perturbed matrices Proceedings of the American Control Conference
  • Meyer , KR . 1966 . On the existence of Lyapunov functions for the problem of Lur’e . SIAM Journal of Control , 3 : 373 – 383 .
  • Narendra , K and Goldwyn , R . 1964 . A geometrical criterion for the stability of certain non-linear non-autonomous systems . IEEE Transactions on Circuit Theory , 11 : 406 – 407 .
  • Shorten , RN and Narendra , K . 2002 . Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems . International Journal of Adaptive Control and Signal Processing , 16 : 709 – 728 .
  • Shorten , RN and Narendra , KS . 2003 . A note on common quadratic Lyapunov functions . IEEE Transactions on Automatic Control , 48 : 618 – 621 .
  • Shorten , RN , Narendra , KS and Mason , O . 2003 . A result on common quadratic Lyapunov functions . IEEE Transactions on Automatic Control , 48 : 110 – 113 .
  • Willems , J . 1973 . The circle criterion and quadratic Lyapunov functions for stability analysis . IEEE Transactions on Automatic Control , 18 : 184

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