Controllability of quasimonotone systems in a positive cone (Q1097851)

The problem of controllability and reachability of quasi-monotone dynamical systems is considered. It is assumed that the controls vanish on the boundary of the domain of variation. Rank conditions for various types of reachability and controllability for linear and nonlinear finite-dimensional systems are presented and proved. Special attention is paid to the controllability in a positive cone, which is motivated by biological applications. An illustrative example is also given. Similar problems have been considered in the papers by \textit{S. H. Saperstone} and \textit{J. A. Yorke} [SIAM J. Control 9, 253-262 (1971; Zbl 0199.483)] and \textit{R. F. Brammer} [ibid. 10, 339-353 (1972; Zbl 0242.93007)].