Stabilization of two-dimensional linear systems by time-delay feedback controls. (English) Zbl 0843.93058

Hu, Bo

Differ. Integral Equ. 9, No. 2, 409-420 (1996).

The author considers the action of a delayed feedback control (1) \(u(t)= Kx (t- \tau)\) on finite-dimensional, controllable, single input linear systems (2) \(\dot x= Ax+ Bu\). The stability analysis is reduced to the study of the roots of a transcendental polynomial. In the two-dimensional case, the author shows that (2) is stabilized by (1) if and only if \(\tau\) is not larger than some upper bound. Such a bound depends on the signs of the coefficients of the characteristic polynomial of \(A\) and they are explicitly computed.

Reviewer: A.Bacciotti (Torino)

MSC:

93D15	Stabilization of systems by feedback
93C05	Linear systems in control theory

Keywords:

stabilization; delay; delayed feedback; linear systems