Approximate positive controllability of positive boundary control systems

Exact and positive controllability of boundary control systems

“…In Section 5 we will see that (6), (7), and (10) allow us to easily compute the controllability map in the situations studied in [16,Sect. 4] and [17,Sect.…”

“…and choosing the control operator B = b := Ψv ∈ C m we are in the situation considered in [16] and [7], see also [6,Sec. 18.4].…”

“…For an example of an application of this approach to population models in biology we refer to [4]. The stability and control problems of linear flows in networks using semigroup approach were investigated in [16,17,25,7]. Our aim here is to further generalize and refine these latter results.…”

Remarks on the approximate positive for Lotka-McKendrick system by positive birth control

“…Under the above assumptions and for u ∈ L 1 loc (R + , U ), the authors in [1,4,5] have been shown that if x is a classical solution of (BCP ), i.e. x(•) ∈ C 1 (R + , X) with x(t) ∈ D(A m ) for all t ≥ 0 satisfying the boundary systems (BCP ), then it is given by the variation of constat formula…”

“…Consequently the controllability in the usual sense is impossible. The notion of approximate positive controllability of boundary positive control systems has been studied in [1,2]. By applying the above theory we study and characterize the approximate positive controllability of boundary positive control of Lotka-McKendrick system.…”