A. M. A. Abou-El-Ela
Department of Mathematics,
Faculty of Science,
Assiut University,
Assiut 71516, Egypt
A. I. Sadek
Department of Mathematics,
Faculty of Science,
Assiut University,
Assiut 71516, Egypt
A. M. Mahmoud
Department of Science and Mathematics,
Faculty of Education, Assiut University,
New Valley, El-khargah 72111, Egypt
In this paper we study the stability of linear non-autonomous time-varying system with multiple delays. Using the Lyapunov functionals method we find sufficient conditions for the exponential stability with a given convergence rate, in terms of linear matrix inequalities or the solution of Riccati differential equations. The results are applied to stabilization problem of linear non-autonomous time-varying control system with multiple delays.