On the Strong-Accessibility Test for Meromorphic Nonlinear Systems

In this paper we show that a couple of matrices A,B (a 'dynamic' and a 'control' matrix), whose components are in general functions of both state and control variables, can be associated to any stationary nonlinear system whose system function is meromorphic (e.g. all components are ratios of analytic functions) in a way consistent with linear systems theory, and such that the test of accessibility (from a point p of the system domain) can be carried out formally as the controllability test for linear systems: the controllability matrix is built up and the full rank condition checked at the point p. The test terminates, giving always an exhaustive answer (yes/no) within a fixed number of steps, a feature not owned by the classical accessibility test, based on the calculation of vectors from an infinite generator of the control Lie algebra. Further, it is proved that the accessibility from a point p implies the accessibility from every point of the largest open connected subset of the system domain including p, which, for the sub class of sigma-pi-systems (in R<formula><tex>$^n$</tex></formula>) can be readily determined as a certain union of orthants of R<formula><tex>$^n$</tex></formula>.