On the Robust Stability of Unforced Nonlinear Systems

A new framework is developed to study the robust stability of nonlinear systems based on operator-theoretic methods. First new representation called zeta
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for nonlinear systems is presented. This new representation turns the nonzero initial state stability problem into input-output stability problem for nonlinear systems. In this representation, uncertainty is described as a set of memoryless nonlinearities. Based on this representation, sufficient condition on the robust global stability of nonlinear systems is derived. Using a new definition for local region of local stability, the derived condition for global stability is extended into local robust stability