On the Stability of Linear Time-Varying Differential Equations

被引：2

作者：

Zaitsev, V. A. ^{[1
]}

Kim, I. G. ^{[1
]}

机构：

[1] Udmurt State Univ, Izhevsk 426034, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2022年 / 319卷 / SUPPL 1期

关键词：

linear differential equations; stability; time-varying system; stable polynomial; Kharitonov's theorem; robust stability; SUFFICIENT CONDITIONS;

D O I：

10.1134/S0081543822060268

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The article discusses the stability of linear differential equations with time-varying coefficients.It is shown that, in contrast to equations with time-invariant coefficients, the condition for the characteristicpolynomial to be Hurwitz for a linear differential equation with time-varying coefficients is neither necessarynor sufficient for the asymptotic stability of the differential equation. It is proved that the analog of Kharitonov'stheorem on robust stability does not hold if the coefficients of the differential equation are time-varying.

引用

页码：S298 / S317

页数：20

共 17 条

[1] NEW SUFFICIENT CONDITIONS FOR THE STABILITY OF SLOWLY VARYING LINEAR-SYSTEMS [J].

AMATO, F ;

CELENTANO, G ;

GAROFALO, F .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1993, 38 (09) :1409-1411

[2]

Bhattacharyya S. P., 1995, Robust control: the parametric approach

[3]

Bylov B. F., 1966, Theory of Lyapunov Exponents and Its Application to Stability Problems

[4]

Coppel WA., 1978, LECT NOTES MATH, DOI 10.1007/BFb0067780

[5]

Demidovich BP., 2008, LECT MATH THEORY STA

[6] SUFFICIENT CONDITIONS FOR STABILITY OF LINEAR TIME-VARYING SYSTEMS [J].

ILCHMANN, A ;

OWENS, DH ;

PRATZELWOLTERS, D .

SYSTEMS & CONTROL LETTERS, 1987, 9 (02) :157-163

[7]

Kharitonov VL., 1979, DIFFER EQNS, V14, P1483

[8]

Levin A. Y., 1993, St. Petersburg Mathematical Journal, V4, P149

[9]

Postnikov M.M., 2004, Stable Polynomials, V2nd

[10]

Rouche N., 1977, Stability theory by liapunovs direct method, DOI 10.1007/978-1-4684-9362-7

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