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Analysis of minimum phase properties for non-affine nonlinear systems

A system can be termed non-minimum phase according to some definitions available in the literature and yet the same system may exhibit stable zero output constrained dynamics. We show that for non-affine nonlinear systems there may not exist a continuous control law which would keep the output identically equal to zero and for which the zero output constrained dynamics are stable, whereas a discontinuous controller which achieves this exists. We give conditions for existence and present a method for design of discontinuous switching controllers which yield stable zero dynamics. In this sense, the results of this paper enlarge the class of non-affine nonlinear systems that can be termed minimum-phase.