Journal of Applied Mathematics and Stochastic Analysis
Volume 15 (2002), Issue 2, Pages 141-150

Stability analysis of nonlinear Lyapunov systems associated with an nth order system of matrix differential equations

K. N. Murty1,2 and Michael D. Shaw1

1Florida Institute of Technology, Department of Mathematical Sciences, Melbourne 32901, FL, USA
2Andhra University, Department of Applied Mathematics, Viskhapatnam, India

Received 1 March 2000; Revised 1 October 2000

Copyright © 2002 K. N. Murty and Michael D. Shaw. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper introduces the notion of Lipschitz stability for nonlinear nth order matrix Lyapunov differential systems and gives sufficient conditions for Lipschitz stability. We develop variation of parameters formula for the solution of the nonhomogeneous nonlinear nth order matrix Lyapunov differential system. We study observability and controllability of a special system of nth order nonlinear Lyapunov systems.