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Equivalent predictions of the circle criterion and an optimum quadratic form for a second-order system

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2 Author(s)
Tsoi, /A/. ; University of Salford, Salford, England ; Power, H.

It is shown that, for the equation frac{d^{2}u}{dt^{2}} + \mu frac{du}{dt} + g (t,u,frac{du}{dt}) {u + \lambda frac{du}{dt}} = 0 , the maximum value of β for which asymptotic stability can be guaranteed with a < g(t, u, du/dt) < \beta (a \geq 0) is the same whether derived by the circle criterion or by means of a quadratic Lyapunov function with constant coefficients, and this maximum value is explicitly evaluated.

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Automatic Control, IEEE Transactions on  (Volume:17 ,  Issue: 4 )