Controllability measure for nonlinear systems in complex region

This paper proposes a controllability measure for nonlinear systems which evaluates a degree of controllability. There are many researches on controllability measure for linear systems. However there exists no measure for nonlinear systems. This paper introduces a theorem about a property of systems which are not strongly accessible and proposes controllability measure based on the theorem. Furthermore this paper demonstrates that the measure relates to a distance to a system which is not strongly accessible which is one of measures of evaluating a degree of controllability. Finally this paper applies the measure to an example system and calculates the controllability measure and the distance of the system.