Opuscula Mathematica
Opuscula Math. 46, no. 1 (2026), 41-54

Wintner-type asymptotic behavior of linear differential systems with a proportional derivative controller

Kazuki Ishibashi
Abstract. This study investigated the asymptotic behavior of linear differential systems incorporating a proportional derivative-type (PD) differential operator. Building on the classical asymptotic convergence property of Wintner, a generalized Wintner-type asymptotic result was established for such systems. The proposed framework encompasses a wide class of time-varying coefficient matrices and extends classical asymptotic theory to equations governed by PD operators. An illustrative example is presented to demonstrate the applicability of the proposed theorem.
Keywords: Wintner-type, asymptotic behavior, linear differential systems, proportional-derivative controller.
Mathematics Subject Classification: 34D05, 26A24.
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About the authors ▼
Kazuki Ishibashi
https://orcid.org/0000-0003-1812-9980
Department of Civil and Environmental Engineering, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima 731-5193, Japan
About the article ▼
Communicated by Josef Diblík.
Received: 2025-08-01.
Revised: 2025-10-14.
Accepted: 2025-12-10.
Published online: 2026-01-27.
Cite this article as ▼
Kazuki Ishibashi, Wintner-type asymptotic behavior of linear differential systems with a proportional derivative controller, Opuscula Math. 46, no. 1 (2026), 41-54, https://doi.org/10.7494/OpMath.202512101.
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