Document Type : Research Paper

Authors

• G. Suresh Kumar ¹
• B. V. Appa Rao ¹
• M. S. N Murthy ²

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 $X^{\prime }=A(t)X+XB(t)+F(t,X)$.

Keywords

• fundamental matrix
• $\mathrm{\Psi }$-bounded
• $\mathrm{\Psi }$-stable
• $\mathrm{\Psi }$-conditional asymptotic stable