LIAPUNOV FUNCTIONAL FOR A MATRIX NEUTRAL DIFFERENCE-DIFFERENTIAL EQUATION WITH ONE DELAY

被引：29

作者：

CASTELAN, WB ^{[1
]}

INFANTE, EF ^{[1
]}

机构：

[1] UNIV FED SANTA CATARINA,DEPT MATEMAT,88000 FLORIANOPOLIS,BRAZIL

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1979年 / 71卷 / 01期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/0022-247X(79)90219-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the matrix neutral difference-differential equation x ̇(t) + A x ̇(t - τ) Bx(t) + Cx(t - τ) we construct a quadratic Liapunov functional which gives necessary and sufficient conditions for the asymptotic stability of the solutions of that equation. We consider a difference equation approximation of the difference-differential equation, and for this difference equation we construct a Liapunov function from which we obtain the desired Liapunov functional by an appropriate limiting process. The Liapunov functional thus obtained gives the best possible estimate for the rates of growth or decay of the solutions of the matrix neutral difference-differential equation. The results obtained are natural generalizations of previous results obtained for a matrix retarded difference-differential equation with one delay. © 1979.

引用

页码：105 / 130

页数：26

共 11 条

[1] Castelan, Infante, On a functional equation arising in the stability theory of difference-differential equations, Quart. Appl. Math., 35, pp. 311-319, (1977)
[2] Coddington, Levinson, Theory of Ordinary Differential Equations, (1955)
[3] Hale, Functional Differential Equations, Appl. Math. Science Series, (1977)
[4] Hale, Ordinary Differential Equations, (1967)
[5] Hale, Stability in linear systems of difference and differential-difference equations, Proceedings of the Conference on Differential Equations, pp. 10-70, (1976)
[6] Hale, Sufficient conditions for stability and instability of autonomoux functional differential equations, J. Differential Equations, 1, pp. 452-482, (1965)
[7] Infante, Castelan, A Liapunov functional for a matrix differential-difference equation, J. Differential Equations, 29, pp. 439-451, (1978)
[8] Lancaster, Theory of Matrices, (1969)
[9] Melvin, A class of neutral functional differential equations, J. Differential Equations, 12, pp. 524-534, (1972)
[10] Melvin, Stability properties of functional differential equations, J. Math. Anal. Appl., 48, pp. 749-763, (1974)

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