مرکز منطقه ای اطلاع رساني علوم و فناوري - Improving the predictions of the circle criterion by combining quadratic forms

DocumentCode :

810950

Title :

Improving the predictions of the circle criterion by combining quadratic forms

Author :

Power, H.M. ; Tsoi, A.C.

Author_Institution :

University of Salford, Salford, England

Volume :

Issue :

fYear :

1973

fDate :

2/1/1973 12:00:00 AM

Firstpage :

Lastpage :

Abstract :

By using a Lyapunov function which consists of different quadratic forms in various sectors of the ( $u, (du/d\\tau )$ ) plane, the prediction of the circle criterion that the null solution of $(d^{2}u/d\\tau ^{2}) + 2(du/d\\tau ) + f(\\tau , u, (du/d\\tau ))\\cdotp u = 0$ is asymptotically stable for $0 \\leq \\alpha < f(\\cdotp) < \\beta$ , with $\\beta = (\\sqrt {\\alpha } + 2)^{2}$ , is improved to $\\beta = [{frac{(\\sqrt {\\alpha } + 1)^{2} + 1 + \\sqrt {(\\sqrt {\\alpha } + 1)^{4} + 2 (\\sqrt {\\alpha } + 1)^{2} + 5}}{2}}^{frac{1}{2}} + 1 ]^{2}$ .

Keywords :

Asymptotic stability; Circle stability criterion; Lyapunov functions; Nonlinear systems, time-varying; Time-varying systems, nonlinear; Algebra; Equations; Lyapunov method;

fLanguage :

English

Journal_Title :

Automatic Control, IEEE Transactions on

Publisher :

ieee

ISSN :

0018-9286

Type :

jour

DOI :

10.1109/TAC.1973.1100204

Filename :

1100204

Link To Document :

https://search.ricest.ac.ir/dl/search/defaultta.aspx?DTC=49&DC=810950