Characterization by detectability inequality for periodic stabilization of linear time-periodic evolution systems

Xu, Yashan

doi:10.48550/arxiv.2010.12137

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2020

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“…About the characterizations on the exponential stabilization for infinite-dimensional linear timeinvariant systems, we would like to mention [25,33]. About the characterizations on the periodically exponential stabilization for infinite-dimensional linear time-periodic systems, we mention works [38,39,41].…”

Section: Related Workmentioning

confidence: 99%

Characterizations of complete stabilizability

Liu¹,

Wang²,

Xu³

et al. 2020

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We present several characterizations, via some weak observability inequalities, on the complete stabilizability for a control system [A, B], i.e., y ′ (t) = Ay(t) + Bu(t), t ≥ 0, where A generates a C0-semigroup on a Hilbert space X and B is a linear and bounded operator from another Hilbert space U to X. We then extend the aforementioned characterizations in two directions: first, the control operator B is unbounded; second, the control system is time-periodic. We also give some sufficient conditions, from the perspective of the spectral projections, to ensure the weak observability inequalities. As applications, we provide several examples, which are not null controllable, but can be verified, via the weak observability inequalities, to be completely stabilizable.

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