On the Robust Stability of Unforced Nonlinear Systems

摘要

A new framework is developed to study the robust stability of nonlinear systems based on operator-theoretic methods. First new representation called zeta_A 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