Journal of Applied Mathematics and Stochastic Analysis
Volume 15 (2002), Issue 2, Pages 141-150
Stability analysis of nonlinear Lyapunov systems associated with
an th order system of matrix differential equations
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 th 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 th order matrix Lyapunov differential system. We
study observability and controllability of a special system of th order nonlinear Lyapunov systems.