après un certains temps et de possibles larges déviations, toute trajectoire du système convergera vers son état d'équilibre. Cependant, un système attractif n'est pas nécessairement stable, au sens de la définition A.1.2, c'est pourquoi on introduit alors la notion de stabilité asymptotique qui garantit que l'état du système converge vers son état d'équilibre sans trop s'en éloigner ,
appuie sur une observation fondamentale de la physique : si l'énergie totale d'un système est dissipée de manière continue alors le système devra rejoindre finalement un point d'équilibre. On pourra donc conclure à la stabilité d'un système par l'examen de la variation d'une fonction scalaire V ,
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