Rapid stabilizability of delayed infinite-dimensional control systems

In this paper, the rapid stabilizability of linear infinite-dimensional control system with constant-valued delay is studied. Under assumptions that the state operator generates an immediately compact semigroup and the coefficient of the delay term is constant, we mainly prove the following two results: (i) the delay does not affect rapid stabilizability of the control system; (ii) from the perspective of observation-feedback, it is not necessary to use historical information to stabilize the control system when the system is rapidly stabilizable. Some applications are given.

💡 Research Summary

Rapid Stabilizability of Delayed Infinite‑Dimensional Control Systems investigates whether a constant‑valued delay term influences the ability to achieve arbitrarily fast exponential decay (rapid stabilizability) for linear control systems evolving in a Hilbert space. The authors consider a state operator (A) that generates an immediately compact (C_{0})-semigroup and a control operator (B) that maps the control space (U) into the extrapolation space (X_{-1}). The system under study is

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