New Stability Criteria for Linear Volterra Time-varying
            Integro-differential Equations

Anh, Tran The; Ngoc, Pham Huu Anh

doi:10.11650/tjm/7812

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Solution Bounds Of Time-varying Linear Integrodifferential S...2

Linear Volterra Differential Equations1

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2017

2023

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Cited by 9 publications

(3 citation statements)

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“…The following lemma presents conditions for the exponential convergence of linear time-varying integro-differential systems with exponentially decaying perturbations. The proof, which is omitted here, follows similar steps as in [23] and the Grönwall's inequality.…”

Section: Solution Bounds Of Time-varying Linear Integrodifferential S...mentioning

confidence: 99%

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A time-varying matrix solution to the Brockett decentralized stabilization problem

Sun¹

2023

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This paper proposes a time-varying matrix solution to the Brockett stabilization problem. The key matrix condition shows that if the system matrix product CB is a Hurwitz H-matrix, then there exists a time-varying diagonal gain matrix K(t) such that the closed-loop minimum-phase linear system with decentralized output feedback is exponentially convergent. The proposed solution involves several analysis tools such as diagonal stabilization properties of special matrices, stability conditions of diagonal-dominant linear systems, and solution bounds of linear time-varying integro-differential systems. A review of other solutions to the general Brockett stabilization problem (for a general unstructured time-varying gain matrix K(t)) and a comparison study are also provided.

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Section: Solution Bounds Of Time-varying Linear Integrodifferential S...mentioning

confidence: 99%

“…Theorem 2: (Conditions for exponential convergence of linear integro-differential systems, [23]) Consider the following integro-differential system…”

Section: Solution Bounds Of Time-varying Linear Integrodifferential S...mentioning

confidence: 99%