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

摘要: 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 , maximum value of β which asymptotic stability can be guaranteed with a same whether derived by circle criterion or means quadratic Lyapunov function constant coefficients, and this explicitly evaluated.