Stabilization of Linear Sampled‐Data Systems by a Time‐Delay Feedback Control

We consider one-dimensional, time-invariant sampled-data linearsystems with constant feedback gain, an arbitrary fixed time delay, whichis a multiple of the sampling period and a zero-order hold for reconstructingthe sampled signal of the system in the feedback control. We obtainsufficient conditions on the coefficients of the characteristic polynomial associatedwith the system. We get these conditions by finding both lowerand upper bounds on the coefficients. These conditions let us give both anestimation of the maximum value of the sampling period and an intervalon the controller gain that guarantees the stabilization of the system