We consider the problem of controlling linear systems with scalar input by means of feedback from the delayed state. A novel scheme for computing the gain that assigns the dominant eigenvalue of the resulting system is presented. The proposed approach is appealing for its simplicity and it can be applied to a variety of situations, such as delayed output measurements or time delay in the input, with both fixed and variable known delay functions. It is possible to assign the same dominant eigenvalue for an interval of delays, and the bound on the delay is expressed through sufficient, and in some cases necessary, conditions that are easy to check. The resulting control is therefore robust with respect to the delay.

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). © 2013 IFAC.

Partial sprectum assignment for systems with delayed state feedback

GERMANI, Alfredo;MANES, COSTANZO
2013-01-01

Abstract

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). © 2013 IFAC.
2013
We consider the problem of controlling linear systems with scalar input by means of feedback from the delayed state. A novel scheme for computing the gain that assigns the dominant eigenvalue of the resulting system is presented. The proposed approach is appealing for its simplicity and it can be applied to a variety of situations, such as delayed output measurements or time delay in the input, with both fixed and variable known delay functions. It is possible to assign the same dominant eigenvalue for an interval of delays, and the bound on the delay is expressed through sufficient, and in some cases necessary, conditions that are easy to check. The resulting control is therefore robust with respect to the delay.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/89185
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