A hybrid approach to nonlinear system stability and performance

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Abstract
The problems of stability and performance for nonlinear feedback systems are examined. A hybrid approach that combines input‐output and state‐space theories is proposed. Within this framework the notions of dynamic gain and dynamic incremental gain of a nonlinear operator are reexamined and their inability to accurately reflect the dynamic behavior of a physical system is demonstrated. The concepts of dynamic gain and dynamic incremental gain over sets are introduced and their connection to a physical system's dynamic behavior is established. Theorems are developed that allow the systematic computation of these gains through nonsmooth optimal control theory. Illustrative examples are provided throughout the paper.