\(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems
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Authors
M. S. N. Murty
- Department of Applied Mathematics, Acharya Nagarjuna University-Nuzvid Campus, Nuzvid-521201, Andhra Pradesh, India.
G. Suresh Kumar
- Department of Mathematics, Koneru Lakshmaiah University, Vaddeswaram, Guntur, Andra Prdesh, India.
Abstract
In this paper, first we convert the non-linear matrix Lyapunov system into a Kronecker product matrix
system with the help of Kronecker product of matrices. Then, we obtain sufficient conditions for \(\Psi\)-asymptotic stability and \(\Psi\)-uniform stability of the trivial solutions of the corresponding Kronecker product
system.
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ISRP Style
M. S. N. Murty, G. Suresh Kumar, \(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 2, 115--125
AMA Style
Murty M. S. N., Kumar G. Suresh, \(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems. J. Nonlinear Sci. Appl. (2012); 5(2):115--125
Chicago/Turabian Style
Murty, M. S. N., Kumar, G. Suresh. "\(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems." Journal of Nonlinear Sciences and Applications, 5, no. 2 (2012): 115--125
Keywords
- Matrix Lyapunov system
- Kronecker product
- Fundamental matrix
- \(\Psi\)-asymptotic stability
- \(\Psi\)-(uniform) stability.
MSC
References
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[1]
O. Akinyele, On partial stability and boundedness of degree k, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 65 (1978), 259-264.
-
[2]
A. Constantin, Asymptotic properties of solutions of differential equations, Analele Universităţii din Timişoara, Seria Ştiin ţe Matematice, (1992), 183-225.
-
[3]
A. Diamandescu, On the \(\Psi\)- stability of Nonlinear Volterra Integro-differential System, Electronic Journal of Differential Equations, 2005 (56) (2005), 1-14.
-
[4]
A. Diamandescu, On the \(\Psi\)- asymptotic stability of Nonlinear Volterra Integro-differential System, Bull. Math. Sc. Math.Roumanie, Tome., 46(94) (1-2) (2003), 39-60.
-
[5]
A. Graham, Kronecker Products and Matrix Calculus: with applications, Ellis Horwood Series in Mathematics and its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York (1981)
-
[6]
J. Morchalo, On \(\Psi-L_p\)-stability of nonlinear systems of differential equations, Analele Ştiinţifice ale Universităţii ''Al. I. Cuza'' Iaşi, Tomul XXXVI, s. I - a, Matematicăf., 4 (1990), 353-360.
-
[7]
M. S. N. Murty, G. Suresh Kumar, On \(\Psi\)-Boundedness and \(\Psi\)-Stability of Matrix Lyapunov Systems, Journal of Applied Mathematics and Computing, Springer, 26 (2008), 67-84.
-
[8]
[8] M. S. N. Murty, G. S. Kumar, P. N. Lakshmi, D. Anjaneyulu, On \(\Psi\)-instability of Non-linear Matrix Lyapunov Systems, , Demonstrtio Mathematica, 42 (4) (2009), 731-743.