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.


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