TY  - JOUR
ID  - Ishibashi2023
LB  - Ishibashi2023
AU  - Ishibashi, Kazuki
TI  - Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations
ST  - Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 1
SP  - 67
EP  - 79
DO  - https://doi.org/10.7494/OpMath.2023.43.1.67
UR  - https://doi.org/10.7494/OpMath.2023.43.1.67
AB  - The proportional derivative (PD) controller of a differential operator is commonly referred to as the conformable derivative. In this paper, we derive a nonoscillation theorem for damped linear differential equations with a differential operator using the conformable derivative of control theory. The proof of the nonoscillation theorem utilizes the Riccati inequality corresponding to the equation considered. The provided nonoscillation theorem gives the nonoscillatory condition for a damped Euler-type differential equation with a PD controller. Moreover, the nonoscillation of the equation with a PD controller that can generalize Whittaker-Hill-type equations is also considered in this paper. The Whittaker-Hill-type equation considered in this study also includes the Mathieu-type equation. As a subtopic of this work, we consider the nonoscillation of Mathieu-type equations with a PD controller while making full use of numerical simulations.
KW  - nonoscillation
KW  - proportional derivative controller
KW  - Riccati technique
KW  - Mathieu equation
KW  - Whittaker-Hill equation
SN  - 1232-9274
ER  -