Strong stabilization of neutral functional differential equations. (English) Zbl 1005.93026

Hale, Jack K.; Verduyn Lunel, Sjoerd M.

IMA J. Math. Control Inf. 19, No. 1-2, 5-23 (2002).

Feedback stabilization of a particular type of neutral ordinary differential equations (ODEs) with constant delays is studied by an abstract method, claimed to be ‘unifying’. In the systems in question, the velocity depends on the past velocity and on external inputs. It depends neither on the past acceleration nor on any constraint. Neutral ODEs deriving from a Hamiltonian with delay, frequent in practice, are not even mentioned.
Although several fundamental properties of ODEs with variously shifted arguments were already known to Euler and Lagrange, the earliest cited reference dates back only to a SIAM paper of 1983.
Not a single genuinely applied system is examined showing the superiority of the promoted ‘unifying’ approach over any current ‘pedestrian’ one.

Reviewer: I.Gumowski (Thoiry)

MSC:

93C25	Control/observation systems in abstract spaces
93D15	Stabilization of systems by feedback

Keywords:

Banach space approach; systems in abstract space; feedback stabilization; neutral ordinary differential equations; constant delays