Liapunov functions for autonomous systems of second order

Weighted Liapunov Functions for a Class of Third - Order Autonomous Differential Equations

Regularity of Liapunov Functions for Stable Systems

We consider the problem of characterizing those systems which admit (weak) Liapunov functions with nice analytic properties. Our investigation gives a rather complete picture of the situation for the one-dimensional case.

Algebraic curve solution for second-order polynomial autonomous systems

The Method of Liapunov Functions for Nonlinear Input Systems

The purpose of this work is to survey some possible deenitions of external stability for nonlinear systems and to provide the basic tools for investigating their relationship and dependence on internal stability properties. In particular, we review some early and more recent results about converse Liapunov theorems. To this respect, some improvements are pointed out without proof.

Extending Liapunov's Second Method to Non-lipschitz Liapunov Functions

where/ : U—>R is continuous on the open set UC.RXR, is frequentlystudied by means of a continuous function V: U—*R. I t is sometimes unnecessary to know the solutions explicitly. If for example V is independent of /, V(xo) = 0 for some #o, V(x)>0 for XT^X^ and if for each solution of (E), V(</)(t)) is a monotonically decreasing function of t for t^Oy then x0 is a stable critical point of (E...