Global attractivity without stability for Liénard type systems

Global Attractivity without Stability for Liénard Type Systems

We are concerned with some conditions such as the trivial solution of a planar system of differential equations (including the Liénard system) that is globally attractive but not stable. We emphasize the connection with some nonoscillatory conditions. The results are related to the previous ones obtained by Hara in 1993. 2000 Mathematics Subject Classification. 34D45.

Uniform weak attractivity and criteria for practical global asymptotic stability

A subset A of the state space is called uniformly globally weakly attractive if for any neighborhood S of A and any bounded subset B there is a uniform finite time τ so that any trajectory starting in B intersects S within the time not larger than τ . We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attracti...

Necessary conditions for stability and attractivity of continuous systems

Considered in this paper are control systems of the form _ x 1⁄4 f ðx; uÞ. For such systems a number of related necessary conditions for various forms of stability and attractivity are presented. The paper starts by showing that Brockett’s necessary condition for stabilizability via smooth feedback still persists if f is continuous and the class of allowable u increased to include continuous fe...

Global Attractivity of a Family of Max-Type Difference Equations

On the Global Attractivity of a Max-Type Difference Equation