On the stability of a class of unforced nonlinear systems: an operator norm approach

A new framework to study the stability of nonlinear systems is presented. Given a nonlinear system, the authors first decompose it as the feedback interconnection of two operators and a decaying input originated by the initial state. Using these operators, the non-zero initial state stability problem is converted into an input-output stability problem. Based on this approach, sufficient conditions for global stability for unforced nonlinear systems are derived. In the case of local stability, a new method is proposed to estimate the stability region.