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 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 $X' = A(t)X + XB(t) + F(t,X)$.


  • Receive Date: 10 January 2012
  • Revise Date: 08 November 2012
  • Accept Date: 02 January 2013