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

Document Type : Research Paper

Authors

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

Abstract

We provide necessary and sufficient conditions for psi-conditional asymptotic stability of the solution of a linear matrix Lyapunov system and sufficient conditions for psi -conditional asymptotic stability of the solution of a first order non-linear matrix Lyapunov system $X' = A(t)X + XB(t) + F(t,X)$.

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