1. B. Jakubczyk and E.D. Sontag. Controllability of nonlinear discrete-time systems: a Lie-algebraic approach. SIAM J. Control Optim., 28(1):1-33, 1990. [PDF] [doi:http://dx.doi.org/10.1137/0328001] Keyword(s): discrete-time. Abstract:

   This paper presents a geometric study of controllability for discrete-time nonlinear systems. Various accessibility properties are characterized in terms of Lie algebras of vector fields. Some of the results obtained are parallel to analogous ones in continuous-time, but in many respects the theory is substantially different and many new phenomena appear.




2. B. Jakubczyk and E.D. Sontag. Nonlinear discrete-time systems. Accessibility conditions. In Modern optimal control, volume 119 of Lecture Notes in Pure and Appl. Math., pages 173-185. Dekker, New York, 1989. [PDF]



3. A. Arapostathis, B. Jakubczyk, H.-G. Lee, S. I. Marcus, and E.D. Sontag. The effect of sampling on linear equivalence and feedback linearization. Systems Control Lett., 13(5):373-381, 1989. [PDF] [doi:http://dx.doi.org/10.1016/0167-6911(89)90103-5] Keyword(s): discrete-time, sampled-data systems, discrete-time systems, sampling. Abstract:

   We investigate the effect of sampling on linearization for continuous time systems. It is shown that the discretized system is linearizable by state coordinate change for an open set of sampling times if and only if the continuous time system is linearizable by state coordinate change. Also, it is shown that linearizability via digital feedback imposes highly nongeneric constraints on the structure of the plant, even if this is known to be linearizable with continuous-time feedback.

1. B. Jakubczyk and E.D. Sontag. The effect of sampling on feedback linearization. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec.1987, pages 1374-1379, 1987.

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