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

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.

### MSC:

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

### Keywords:

stabilization; delay; delayed feedback; linear systems