On the Ψ – Conditional Stability of Nonlinear Lyapunov Matrix Differential Equations

Diamandescu, Aurel

doi:10.2478/awutm-2014-0004

Abstract

It is proved (necessary and) suficient conditions for Ψ conditional stability of the trivial solution of linear or nonlinear Lyapunov matrix differential equations

References

[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, (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, 46(94), No. 3-4, (2003), 103-119
Search in Google Scholar
[5] A. Diamandescu, On the Ψ instability of nonlinear Lyapunov matrix differential equations, Analele Universităţii de Vest, Timişoara, Seria Matematică - Informatică, XLIX, 1, (2011), 21-37
Search in Google Scholar
[6] A. Diamandescu, On Ψ - stability of a nonlinear Lyapunov matrix differential equations, Electronic Journal of Qualitative Theory Differential Equations, 54, (2009), 1-1810.14232/ejqtde.2009.1.54
Search in Google Scholar
[7] A. Diamandescu, On Ψ - asymptotic stability of nonlinear Lyapunov matrix differential equations, Analele Universităţii de Vest, Timişoara, Seria Matematică - Informatică, L, 1, (2012), 32510.2478/v10324-012-0001-8
Search in Google Scholar
[8] A. Diamandescu, On the Ψ -strong stability of nonlinear Lyapunov matrix differential equations, to appear
Search in Google Scholar
[9] A. Diamandescu, On the Ψ- Exponential Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations, Analele Universităţii de Vest, Timişoara, Seria Matematică - Informatică, LI, 2, (2013), 7-2810.2478/awutm-2013-0012
Search in Google Scholar
[10] M.S.N. Murty and Suresh Kumar, On dichotomy and conditioning for twopoint boundary value problems associated with first order matrix Lyapunov systems, J. Korean Math. Soc., 45, no. 8, (2008), 1361-137810.4134/JKMS.2008.45.5.1361
Search in Google Scholar
[11] M.S.N. Murty and Suresh Kumar, On Ψ- boundedness and Ψ -stability of matrix Lyapunov systems, J. Appl. Math. Comput, 26, (2008), 67-8410.1007/s12190-007-0007-2
Search in Google Scholar
[12] M.S.N. Murty, B. V. Apparao, and Suresh Kumar, Controllability, observability and realizability of matrix Lyapunov systems, Bull. Korean math. Soc., 43, no. 1, (2006), 149-15910.4134/BKMS.2006.43.1.149
Search in Google Scholar
[13] O. Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z., 32, (1930), 703-728 10.1007/BF01194662
Search in Google Scholar

On the Ψ – Conditional Stability of Nonlinear Lyapunov Matrix Differential Equations

Abstract

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