Boundedness theorems by two Liapunov functions

External Stability and Continuous Liapunov Functions

It is well known that external stability of nonlinear input systems can be investigated by means of a suitable extension of the Liapunov functions method. We prove that a complete characterization by means of continuous Liapunov functions is actually possible, provided that the de nition of external stability is appropriately strengthened.

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.

Boundedness Theorems for Dilators and Ptykes

Kechris, A.S., Boundedness theorems for dilators and ptykes, Annals of Pure and Applied Logic 52 (1991) 79-92. The main theorem of this paper is: If f is a partial function from K, to X, which is Pi-bounded, then there is a weakly finite primitive recursive dilator D such that for all infinite a E domu), f(a) s D(a). The proof involves only elementary combinatorial constructions of trees. A gen...

Boundedness Theorems for the Relaxation Method

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...