Open Access

On the Ψ-Conditional Exponential Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations


Cite

[1] R. Bellman, Introduction to Matrix Analysis, McGraw-Hill Book Company, Inc., New York, 1960.Search in Google Scholar

[2] W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Company, Boston, 1965.Search in Google Scholar

[3] A. Diamandescu, On the Ψ conditional stability of the solutions of a nonlinear Volterra integro-differential system, Proceedings of the National Conference on Mathematical Analysis and Applications, (Timişoara, 12-13 Dec. 2000), 89-106.Search in Google Scholar

[4] A. Diamandescu, On the Ψ– Instability of a Nonlinear Volterra Integro-Differential System, Bull. Math. Soc. Sc. Math. Roumanie, Tome 46(94), (2003), 103-119.Search in Google Scholar

[5] A. Diamandescu, On the Ψ– conditional asymptotic stability of the solutions of a nonlinear Volterra integro-differential system, Electronic Journal of Differential Equations, (2007), 1-13.Search in Google Scholar

[6] A. Diamandescu, On the Ψ– instability of nonlinear Lyapunov matrix differential equations, Analele Universităţii de Vest, Timişoara, Seria Matematică-Informatică, XLIX, (2011), 21-37.Search in Google Scholar

[7] A. Diamandescu, On Ψ– stability of a nonlinear Lyapunov matrix differential equations, Electronic Journal of Qualitative Theory Differential Equations, (2009), 1-18.10.14232/ejqtde.2009.1.54Search in Google Scholar

[8] A. Diamandescu, On Ψ– asymptotic stability of nonlinear Lyapunov matrix differential equations, Analele Universităţii de Vest, Timişoara, Seria Matematică - Informatică, L, (2012), 3-25.10.2478/v10324-012-0001-8Search in Google Scholar

[9] A. Diamandescu, On the Ψ– strong stability of nonlinear Lyapunov matrix differential equations, Math. Slovaca, 65, (2015), 555–572.10.1515/ms-2015-0040Search in Google Scholar

[10] A. Diamandescu, On the Ψ– Exponential Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations, Analele Universităţii de Vest, Timişoara, Seria Matematică - Informatică, LI, (2013), 07-28.10.2478/awutm-2013-0012Search in Google Scholar

[11] A. Diamandescu, On the Ψ-Conditional Stability of Nonlinear Lyapunov Matrix Differential Equations, Analele Universităţii de Vest, Timişoara, Seria Matematică - Informatică, LII, (2014), 41-64.10.2478/awutm-2014-0004Search in Google Scholar

[12] A. Diamandescu, On the Ψ- Conditional Asymptotic Stability of Nonlinear Lyapunov Matrix Differential EquationsSearch in Google Scholar

[13] A. Diamandescu, On the Ψ-Conditional Exponential Asymptotic Stability of the Solutions of a Nonlinear Volterra Integro-differential System, Analele Universităţii din Timişoara, Seria Matematică - Informatică, XV, (2002), 19-44.Search in Google Scholar

[14] W. E. Mahfoud, Boundedness properties in Volterra integro-differential systems, Proc. Amer. Math. Soc., 100, (1987), 37–45.10.1090/S0002-9939-1987-0883398-3Search in Google Scholar

[15] M.S.N. Murty and G. Suresh Kumar, On dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, J. Korean Math. Soc., 45, (2008), 1361-1378.10.4134/JKMS.2008.45.5.1361Search in Google Scholar

[16] M.S.N. Murty and G. Suresh Kumar, On Ψ– boundedness and Ψ– stability of matrix Lyapunov systems, J. Appl. Math. Comput, 26, (2008), 67-84.10.1007/s12190-007-0007-2Search in Google Scholar

[17] M.S.N. Murty, B. V. Apparao, and G. Suresh Kumar, Controllability, observability and realizability of matrix Lyapunov systems, Bull. Korean math. Soc., 43, (2006), 149 - 159.10.4134/BKMS.2006.43.1.149Search in Google Scholar

[18] O. Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z., 32, (1930), 703-728.10.1007/BF01194662Search in Google Scholar

eISSN:
1841-3307
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Mathematics, General Mathematics