Total controllability for nonlinear perturbed discrete systems
We assume G to be a target set in En, the n-dimensional Euclidean space. A control system is said to be totally G-controllable if each point of the state space En can be steered to G in finite time t1 (0≤ t1≤∞) and thereafter stabilized in G for all time t2 ≥ t1 (t2≤ ∞). In this paper we adopt Leray-Schauder fixed point theorem to develop sufficient conditions, which guarantee that whenever an unperturbed nonlinear discrete system is totally G-controllable, then so is its perturbation.
Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 255-258