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

Xu, Yashan

doi:10.1016/j.sysconle.2021.104871

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…Stabilization is one of the most important objectives in control theory. There are two important subjects on stabilization for linear control systems: The first one is to find sufficient conditions/equivalent conditions on stabilizability, such as resolvent conditions (see, for instance, [7,8,13,16]) and weak observability inequalities (see [14,21,26]). The second one is to design feedback laws (see, for instance, [6,10,11,12,18,19,23,24,27]).…”

Section: Motivationmentioning

confidence: 99%

Feedback law to stabilize linear infinite-dimensional systems

Ma¹,

Wang²,

Yu³

2022

Preprint

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We design a kind of feedback law to stabilize a linear infinite-dimensional control system, where the state operator generates a C0-group and the control operator is unbounded. Our feedback law is based on the integration of a mutated Gramian operator-valued function. In the structure of the aforementioned mutated Gramian operator, we utilize the weak observability inequality in [21,14] and borrow some idea used to construct generalized Gramian operators in [11,23,24]. Unlike most related works where the exact controllability is required, we only assume the above-mentioned weak observability inequality which is equivalent to the stabilizability of the system.

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Section: Motivationmentioning

confidence: 99%

Feedback law to stabilize linear infinite-dimensional systems

Ma¹,

Wang²,

Yu³

2022

Preprint

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“…Stabilization is one of the most important objectives in control theory. There are two important subjects in stabilization for linear control systems: The first one aims to find sufficient conditions/equivalent conditions on stabilizability, such as resolvent conditions (see, e.g., [7,8,14,16]) and weak observability inequalities (see [13,21,26]). The second one aims to design feedback laws (see, e.g., [6,10,11,12,18,19,23,24,27]).…”

Section: Introductionmentioning

confidence: 99%

Feedback law to stabilize linear infinite-dimensional systems

Ma¹,

Wang²,

Yu³

2023

MCRF

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<p style='text-indent:20px;'>We design a new feedback law to stabilize the linear infinite-dimensional control system, where the state operator generates a <inline-formula><tex-math id="M1">\begin{document}$ C_0 $\end{document}</tex-math></inline-formula>-group, and the control operator is unbounded. Our feedback law is based on the integration of a mutated Gramian operator-valued function. In the structure of the aforementioned mutated Gramian operator, we utilize the weak observability inequality in [<xref ref-type="bibr" rid="b21">21</xref>,<xref ref-type="bibr" rid="b13">13</xref>] and borrow some idea used to construct generalized Gramian operators in [<xref ref-type="bibr" rid="b11">11</xref>,<xref ref-type="bibr" rid="b23">23</xref>,<xref ref-type="bibr" rid="b24">24</xref>]. Unlike most related works where the exact controllability is required, we only assume the above-mentioned weak observability inequality, which is equivalent to the stabilizability of the system.</p>

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