Minimal polynomial realizations

J. Baillieul, The geometry of homogeneous polynomial dynamical systems,Nonlinear Anal.,4 (1980), 879–900.

J. Baillieul, Controllability and observability of polynomial dynamical systems,Nonlinear Anal.,5 (1981), 543–552.

Z. Bartosiewicz, A new setting for polynomial continuous time systems, and a realization theorem,IMA J. Math. Control Inf.,2 (1985), 71–80.

Z. Bartosiewicz, Realizations of polynomial systems, inAlgebraic and Geometric Methods in Nonlinear Control Theory (M. Fliess and M. Hazewinkel, eds.), pp. 45–54, Reidel, Dordrecht, 1986.

Z. Bartosiewicz, On polynomial continuous time systems, inTheory and Applications of Nonlinear Control Systems (C. Byrnes and A. Lindquist, eds), pp. 293–299, North-Holland, Amsterdam, 1986.

Z. Bartosiewicz, Ordinary differential equations on real affine varieties,Bull. Polish Acad. Sci. Math.,35 (1987), 13–18.

M. Fliess and I. Kupka, A finiteness criterion for nonlinear input-output differential systems,SIAM J. Control Optim.,21 (1983), 721–728.

J. Gauthier and G. Bornard, Global realizations of analytic input-output mappings,SIAM J. Control Optim.,24 (1986), 509–521.

B. Jakubczyk, Existence and uniqueness of realizations of nonlinear systems,SIAM J. Control Optim.,18 (1980), 455–471.

I. Shafarevich,Basic Algebraic Geometry, Springer-Verlag, Berlin, 1977.

E. Sontag,Polynomial Response Maps, Springer-Verlag, Berlin, 1979.

E. D. Sontag and Y. Rouchaleau, On discrete-time polynomial systems,Nonlinear Anal. 1 (1976), 55–64.

H. Sussmann, Existence and uniqueness of minimal realizations of nonlinear systems,Math. Systems Theory,10 (1977), 263–284.