Steady-states control in positive nonlinear normalized models of weakly formalized systems

The paper considers the existence of steady-states (asymptotically stable) in positive nonlinear normalized models (PNM) and control for such states in positive orthant $K$ of $R^n$. The graph model of PNM is a functional graph. Using the notion of admissible control (with coordinates in $(0,1]$) a convexity of stable states set in PNM generated by admissible controls has been proved. The issues of PNM movement from any initial state in $K$ to some predetermined stable state in $K$ have been solved (in asymptotical sense) for open-loop PNM and for PNM with linear state feedback. The appropriate procedures are illustrated by numerical example.