PBH tests for nonlinear systems

Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov-Belevitch-Hautus (PBH) controllability/observability test to nonlinear accessibility/observability. Our PBH accessibility/observability test is equivalent to the accessibility/observability rank condition under a stranded assumption.