[en] control systems ; differential equations ; time-variance ; observability ; asymptotic stability ; circle criterion
[en] This paper presents some new criteria for uniform and non uniform asymtotic stability of equilibria for time-variant differential equations and this within a Liapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Liapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since - after establishing the invariance of observability under output injection - this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.