A local form of small gain theorem and analysis of feedback Volterra systems

The requirement of evaluating a gain over the entire signal space is one of the restrictions in the traditional small gain theorem. In this paper, a local form of small gain theorem is presented. It yields a bound on the external signal that guarantees that the magnitude of the specified signal along the closed loop stays within a certain region and hence it is useful in addressing the signal magnitude dependent stability problem. The theorem is used to analyze the feedback properties of a Volterra series system as well as an inverse (or pseudo inverse) Volterra system. Improvement over existing results is demonstrated, both theoretically and via numerical examples