On controllability of discrete-time bilinear systems

Approximately nearly controllability of discrete-time bilinear control systems with control input characteristic

“…Some recent notable sequence works on bilinear control systems have been carried out by Tie and his co-authors [10,11,8,12]. In [10,12] they consider the following discrete-time bilinear systems with a single input:…”

“…For nonlinear control systems, however, exact controllability in general either requires very strong assumptions on systems/controls or simply fails to exist. For example, it has been shown in [8] that the production storage management model mentioned above is always not exactly controllable when n ≥ 3. Moreover, exact controllability may not be necessary in some applications.…”

Comments on “A Controllability Counterexample” and the Continuation Lemma

“…If for two states ξ, η in M n there is an integer T and an T -control U T such that using (2) we get x(T ) = F T (ξ, U T ) = η, we say η is attainable from ξ and that it belongs to the T -attainable set A T ξ = F T (ξ, R T ) (the set of points that can be reached from ξ in exactly T steps). The attainable set is A ξ = t∈N F t (ξ, R t ).…”

Banach fixed-point theorem in semilinear controllability problems – a survey

“…A few years later this notion was extended to infinite-dimensional systems [4,5]. Over the last decade the controllability has been extensively studied both for finite and infinite dimensional systems [6][7][8][9][10][11][12][13][14][15][16][17][18]. In the case of finitedimensional systems notions of complete and approximate controllability coincide.…”

“…The sufficient conditions for controllability of nonlinear systems in infinite-dimensional spaces may be found in [7][8][9][10][24][25][26][27].…”