zbMATH — the first resource for mathematics

Stability of neutral delay-differential systems: Boundary criteria. (English) Zbl 0913.34060
For linear neutral delay differential equations of the form \[ \dot{x}(t)=Ax(t)+Bx(t-\tau)+C\dot{x}(t-\tau), \] where \(x:{\mathbb{R}}_+\to{\mathbb{R}}^n\) is an unknown function, \(A\), \(B\) and \(C\) are constant \(n\times n\)-matrices and \(\tau=\text{ const}>0\), a series of delay dependent asymptotical stability criteria are given. The criteria are based on the evaluation of a real-valued function on the boundary of a rectangle in the complex plane.

34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations
34K10 Boundary value problems for functional-differential equations
Full Text: DOI
[1] Gopalsamy, K., Stability and oscillations in delay differential equations of population dynamics, (1992), Klumwer Academic Publishers Boston · Zbl 0752.34039
[2] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional differential equations, (1993), Springer Verlag New York · Zbl 0787.34002
[3] Kolmanovskii, V.; Myshkis, A., Applied theory of functional differential equations, (1992), Klumwer Academic Publishers Dordrecht · Zbl 0917.34001
[4] Hu, G.-Di; Hu, G.-Da, Some simple stability criteria of neutral delay-differential systems, Appl. math. comput., 80, 257-271, (1996) · Zbl 0878.34063
[5] Li, L.M., Stability of linear neutral delay-differential systems, Bull. austral. math. soc, 38, 339-344, (1988) · Zbl 0669.34074
[6] Khusainov, D.Ya.; Yun’kova, E.A., Investigation of the stability of linear systems of neutral type by the Lyapunov function method, Diff. uravn, 24, 613-621, (1988) · Zbl 0674.34077
[7] Hu, G.-Di; Hu, G.-Da, Stability of discrete-delay systems: boundary criteria, Appl. math. comput., 80, 95-104, (1996) · Zbl 0874.93084
[8] Lancaster, P.; Tismenetsky, M., The theory of matrices, (1985), Academic Press Orlando, Florida · Zbl 0516.15018
[9] Desoer, C.A.; Vidyasagar, M., Feedback systems: input-output properties, (1975), Academic Press New York · Zbl 0327.93009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.