×

zbMATH — the first resource for mathematics

Some new simple stability criteria of linear neutral systems with a single delay. (English) Zbl 1112.34058
From the summary: This article mainly considers the linear neutral delay-differential systems with a single delay. Using the characteristic equation of the system, new simple delay-independent asymptotic and exponential stability criteria are derived in terms of the matrix measure, the spectral norm and the spectral radius of the corresponding matrices. Numerical examples demonstrate that our criteria are less conservative than those of previous corresponding results.

MSC:
34K20 Stability theory of functional-differential equations
34K06 Linear functional-differential equations
34K40 Neutral functional-differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agarwal, R.P.; Grace, S.R., Asymptotic stability of differential systems of neutral type, Appl. math. lett., 13, 15-19, (2000) · Zbl 0973.34062
[2] Bellen, A.; Guglielmi, N.; Ruehli, A.E., Methods for linear systems of circuit delay-differential equations of neutral type, IEEE trans. circuit syst. I, CAS-46, 212-216, (1999) · Zbl 0952.94015
[3] Cao, D.Q.; Ping He, Sufficient conditions for stability of linear neutral systems with a single delay, Appl. math. lett., 17, 139-144, (2004) · Zbl 1149.34344
[4] Desoer, C.A.; Vidyasagar, M., Feedback systemsinput – output properties, (1975), Academic Press New York · Zbl 0327.93009
[5] Hale, J., Theory of functional differential equations, (1997), Springers New York
[6] Hu, G.D.; Hu, G.D., Some simple criteria for stability of neutral delay-differential systems, Appl. math. comput., 80, 257-271, (1996) · Zbl 0878.34063
[7] Hu, G.D.; Hu, G.D.; Cahlon, B., Algebraic criteria for stability of linear neutral systems with a single delay, J. comput. appl. math., 135, 125-133, (2001) · Zbl 0996.34064
[8] Lancaster, P.; Timenetsky, M., The theory of matrices, (1985), Academic Press Orlando, FL
[9] Li, L.M., Stability of linear neutral delay-differential systems, Bull. aust. math. soc., 38, 339-344, (1988) · Zbl 0669.34074
[10] Niculescu, S.-I., On delay-dependent stability under model transformations of some neutral linear systems, Internat. J. control, 74, 609-617, (2001) · Zbl 1047.34088
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.