On Psi-conditional asymptotic stability of first order nonlinear matrix Lyapunov system

Document Type : Research Paper


1 Department of Mathematics, Konenu Lakshmaiah University, Green Fields, Vaddeswaram-522 502, Guntur Dt., Andhra Pradesh, India.

2 Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar 522510, Guntur, Andhrapradesh, ,India.


We provide necessary and sucient conditions for psi-conditional as-
ymptotic stability of the solution of a linear matrix Lyapunov system and sucient
conditions for psi -conditional asymptotic stability of the solution of a rst order
non-linear matrix Lyapunov system X0 = A(t)X + XB(t) + F(t;X).