Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 4, Pages 209-226
The stability of nonlinear systems is analyzed by the direct Lyapunov's
method in terms of Lyapunov matrix functions. The given paper surveys the
main theorems on stability, asymptotic stability and nonstability. They are
applied to systems of nonlinear equations, singularly-perturbed systems and
hybrid systems. The results are demonstrated by an example of a two-component system.