مرکز منطقه ای اطلاع رساني علوم و فناوري - Equivalent predictions of the circle criterion and an optimum quadratic form for a second-order system

DocumentCode :

809550

Title :

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

Author :

Tsoi, A. ; Power, H.

Author_Institution :

University of Salford, Salford, England

Volume :

Issue :

fYear :

1972

fDate :

8/1/1972 12:00:00 AM

Firstpage :

565

Lastpage :

566

Abstract :

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.

Keywords :

Asymptotic stability; Circle stability criterion; Lyapunov methods; Nonlinear systems, time-varying; Time-varying systems, nonlinear; Asymptotic stability; Automatic control; Differential equations; Feedback; Functional analysis; Lyapunov method; Nonlinear equations; Stability analysis; Stability criteria; Time varying systems;

fLanguage :

English

Journal_Title :

Automatic Control, IEEE Transactions on

Publisher :

ieee

ISSN :

0018-9286

Type :

jour

DOI :

10.1109/TAC.1972.1100066

Filename :

1100066

Link To Document :

https://search.ricest.ac.ir/dl/search/defaultta.aspx?DTC=49&DC=809550