Partial Spectrum Assignment for Systems with Delayed State Feedback

We consider the problem of controlling a linear system when the state is available with a non-negligible delay (delayed-state-feedback control). In such conditions, the resulting closed-loop system is always a time-delay-system. The solution proposed in this paper consists in partially assigning the spectrum of the closed-loop system while ensuring the exponential zero-state stability with a prescribed decay rate. The proposed approach is appealing for its simplicity and can be applied in both cases of constant and time-varying delays. Sufficient stability conditions, that in some cases are also necessary, are provided. Such conditions allow to easily compute a lower bound, and in some cases the exact value, of the maximum delay that ensures the prescribed closed-loop behavior (Partial Spectrum Assignment with prescribed exponential stability).