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IASI Research Report n. 19-05 (Previous Next) Francesco Carravetta,

Sarafrazi M.A.,

Bartosiewicz Z.,

Kotta Ü.AN ALMOST-EVERYWHERE CONTROLLABILITY CRITERION FOR NONLINEAR DIFFERENTIAL MEROMORPHIC SYSTEMSABSTRACT 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 and the time derivation operator, 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 set of generators of the control Lie algebra. Further, a generic feature of accessibility is proven: the accessibility from a point p of the system analyticity domain implies the accessibility from almost every point of the domain connected component including p. Such components, for the subclass of ??-systems (in R^n) can be readily determined as a certain union of orthants of R^n.