Qualitative analysis of nonlinear systems by the method of matrix Lyapunov functions (Q1898321)

The author studies the system (1) \(x'= f(t, x)\) on a domain in \(\mathbb{R}^n\). He develops the notion of a matrix Lyapunov function as a natural generalization of ordinary scalar and vector Lyapunov functions. The main application is to give sufficient conditions for the asymptotic stability of the origin for a large class of equations which are perturbations of (1), when (1) is a ``large scale'' system.