On (phi)-instability of non-liner matrix Lyapunov systems

• Autorzy: Murty M. , Kumar G. , Lakshmi P. , Anjaneyulu
• Języki publikacji: EN

Abstrakty

EN

We prove necessary and sufficient conditions for phi-instability of trivial solutions of linear matrix Lyapunov systems and also sufficient conditions for phi-instability of trivial solutions of non-linear matrix Lyapunov systems.

Słowa kluczowe

EN

fundamental matrix; matrix Lyapumov systems

PL

macierz podstawowa; teoria Lyapunova

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 4
• Strony: 731--743
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Murty M.

autor

Kumar G.

autor

Lakshmi P.

autor

Anjaneyulu

• Department of Applied Mathematics Acharya Nagarjuna University-Nuzvid Campus Nuzvid-521201, Andhra Pradesh, India,

Bibliografia

• [1] O. Akinyele, On partial stability and boundedness of degree k, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 65 (1978), 259-264.
• [2] C. Avramescu, Asupra comportării asimptotice a soluţiilor unor ecuaţii funcţionale, Analele Universităţii din Timişoara, Seria Ştiinţe Matematice-Fizice 6 (1968), 41-55.
• [3] A. Constantin, Asymptotic properties of solutions of differential equations, An. Univ. Timişoara, Ser. Ştiinţe Mat. 30, fasc. 2-3 (1992) 183-225.
• [4] W. A. Coppel, On the stability of differential equations, J. London Math. Soc. 38 (1963), 255-260.
• [5] A. Diamandescu, On the Ψ-stability of nonlinear Volterra integro-differential system, Electron. J. Differential Equations 56 (2005), 1-14.
• [6] A. Diamandescu, On the Ψ-instability of nonlinear Volterra integro-differential system, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 46 (94), No. 3-4 (2003), 103-119.
• [7] A. Graham, Kronecker Products and Matrix Calculus; With Applications, Ellis Horwood Ltd. England (1981).
• [8] T. G. Hallam, On asymptotic equivalence of the bounded solutions of two systems of differential equations, Michigan Math. J. 16 (1969), 353-363.
• [9] J. Morchalo, On Ψ-Lp-stability of nonlinear systems of differential equations, An. Stiinţ. Univ. "Al. I. Cuza" Iaşi Ia Mat. 36 (1990) f. 4, 353-360.
• [10] M. S. N. Murty, B. V. Appa Rao, On two point boundary value problems for X=AX+XB, Journal of Ultra Scientist of Physical Sciences 16, No. 2(M) (2004), 223-227.
• [11] M. S. N. Murty, B. V. Appa Rao, G. Suresh Kumar, Controllability, observability and realizability of matrix Lyapunov systems, Bull. Korean. Math. Soc. No. 1 (2006), 149-159.
• [12] M. S. N. Murty, G. Suresh Kumar, On Ψ-boundedness and Ψ-stability of matrix Lyapunov systems, J. App. Math. Comput. 26 (2008), 67-84.