Mathematical Problems in Engineering
Volume 1 (1995), Issue 4, Pages 303-315

Assignment of nonlinear sampled-data dynamics using generalized hold function control

Pierre T. Kabamba and Yao-Shan Hung

Aerospace Engineering Department, The University of Michigan, Ann Arbor 48109-2140, Michigan, USA

Received 21 February 1995

Copyright © 1995 Pierre T. Kabamba and Yao-Shan Hung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper considers the problem of assigning the dynamics of a nonlinear analytic system using nonlinear generalized sampled-data hold function (GSHF) control, in the neighborhood of an equilibrium point. On every sampling interval, the control input consists of a nonlinear time-periodic function applied to the sampled value of the state vector. The nonlinear monodromy map is the state transition map from one sample time to the next. It is shown that this map is arbitrarily assignable by GSHF feedback if and only if the linear part of the system is controllable. Two approaches are proposed to construct a GSHF controller that performs the assignment. The first approach matches the coefficients of the Taylor series expansion of the monodromy map around the equilibrium. The second approach interpolates an optimal control law at several points in the vicinity of the equilibrium. These approaches are illustrated on an example.