Wei, Jiang General solution and observability of singular differential systems with delay. (English) Zbl 1291.34108 Abstr. Appl. Anal. 2013, Article ID 512465, 10 p. (2013). Summary: We study singular differential systems with delay. A general description for the solutions of singular differential systems with delay is given and a necessary and sufficient condition for exact observability of singular differential systems with delay is derived. Cited in 3 Documents MSC: 34K06 Linear functional-differential equations 93B07 Observability × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Hale, J. K.; Lunel, S. M. V., Strong stabilization of neutral functional differential equations, IMA Journal of Mathematical Control and Information, 19, 1-2, 5-23 (2002) · Zbl 1005.93026 · doi:10.1093/imamci/19.1_and_2.5 [2] Zuxiu, Z., Theory of Functional Differential Equations (1994), Hefei, China: AnHui Education Press, Hefei, China [3] Wei, J., The Degenerate Differential Systems with Delay (1998), Hefei, China: University of Anhui Press, Hefei, China [4] Malek-Zavarei, M.; Jamshidi, M., Time-Delay Systems: Analysis, Optimization and Application. Time-Delay Systems: Analysis, Optimization and Application, North-Holland Systems and Control Series, 9, xvi+504 (1987), Amsterdam, The Netherlands: North-Holland, Amsterdam, The Netherlands · Zbl 0658.93001 [5] Răsvan, V., Time-delay systems with remarkable structural properties, IMA Journal of Mathematical Control and Information, 29, 2, 271-289 (2012) · Zbl 1251.93036 · doi:10.1093/imamci/dnr040 [6] Dai, L., Singular Control Systems. Singular Control Systems, Lecture Notes in Control and Information Sciences, 118, x+332 (1989), Berlin, Germany: Springer, Berlin, Germany · Zbl 0669.93034 · doi:10.1007/BFb0002475 [7] Campbell, S. L., Singular Systems of Differential Equations. II. Singular Systems of Differential Equations. II, Research Notes in Mathematics, 61, iii+234 (1982), Boston, Mass, USA: Pitman, Boston, Mass, USA · Zbl 0482.34008 [8] Wang, C.-J.; Liao, H.-E., Impulse observability and impulse controllability of linear time-varying singular systems, Automatica, 37, 11, 1867-1872 (2001) · Zbl 1058.93011 · doi:10.1016/S0005-1098(01)00137-6 [9] Wang, W.; Zou, Y., Analysis of impulsive modes and Luenberger observers for descriptor systems, Systems & Control Letters, 44, 5, 347-353 (2001) · Zbl 0986.93010 · doi:10.1016/S0167-6911(01)00131-1 [10] Wei, J.; Wenzhong, S., Controllability of singular systems with control delay, Automatica, 37, 11, 1873-1877 (2001) · Zbl 1058.93012 · doi:10.1016/S0005-1098(01)00135-2 [11] Wei, J., Eigenvalue and stability of singular differential delay systems, Journal of Mathematical Analysis and Applications, 297, 1, 305-316 (2004) · Zbl 1063.34052 · doi:10.1016/j.jmaa.2004.05.008 [12] Wei, J., A variation formula for time varying singular delay differential systems, Chinese Annals of Mathematics. Series A, 24, 2, 161-166 (2003) · Zbl 1040.34075 [13] Wei, J.; Zheng, Z. X., The general solution for the degenerate differential system with delay, Acta Mathematica Sinica, 42, 5, 769-780 (1999) · Zbl 1024.34051 [14] Wei, J.; Zheng, Z. X., The variation-of-constants formula and the general solution of degenerate neutral differential systems, Acta Mathematicae Applicatae Sinica, 21, 4, 562-570 (1998) · Zbl 0962.34060 [15] Wei, J.; Zheng, Z., On the degenerate differential system with delay, Annals of Differential Equations, 14, 2, 204-211 (1998) · Zbl 0967.34060 [16] Wei, J.; Wang, Z. C., Controllability of singular control systems with delay, Journal of Hunan University. Natural Sciences, 26, 4, 6-9 (1999) · Zbl 0967.93010 [17] Wei, J., Function-controllability of nonlinear singular delay differential control systems, Acta Mathematica Sinica, 49, 5, 1153-1162 (2006) · Zbl 1124.34356 [18] Wei, J., On the solvability of singular differential delay systems with variable coefficients, International Journal of Dynamical Systems and Differential Equations, 1, 4, 245-249 (2008) · Zbl 1167.34369 · doi:10.1504/IJDSDE.2008.023001 [19] Wei, J., The constant variation formulae for singular fractional differential systems with delay, Computers & Mathematics with Applications, 59, 3, 1184-1190 (2010) · Zbl 1189.34153 · doi:10.1016/j.camwa.2009.07.010 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.