There are almost no results in mathematical literature on the exponential stability of third-order delay differential equations. One of the main purposes of the paper is to fill this gap. We propose an approach to the study of stability for third-order delay differential equations. On the basis of these results, new possibilities of stabilization by delay feedback input control are proposed.
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http://dx.doi.org/10.1186/s13660-018-1930-5 | DOI Listing |
Heliyon
January 2025
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan.
This paper addresses the challenges of maintaining stability in heterogeneous vehicle platooning under the influence of communication disruptions caused by Byzantine attacks within a leader-follower framework. To enhance resilience, we propose a nonlinear control strategy tailored for a third-order heterogeneous dynamic model, integrating leader-follower interconnections with adaptable control gains. Utilizing a constant time headway spacing policy with gap adjustments, we derive control gains that secure internal platoon stability.
View Article and Find Full Text PDFJ Chem Phys
November 2024
Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, USA.
Methods of quantifying the electrostatics of charged interfaces are important in a range of research areas. The surface-selective nonlinear optical technique second harmonic generation (SHG) is a sensitive probe of interfacial electrostatics. Recent work has shown that detection of the SHG phase in addition to its amplitude enables direct quantification of the interfacial potential.
View Article and Find Full Text PDFSci Rep
November 2024
Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta, 31734, Egypt.
This study aims to demonstrate the behaviors of a two degree-of-freedom (DOF) dynamical system consisting of attached mass to a nonlinear damped harmonic spring pendulum with a piezoelectric device. Such a system is influenced by a parametric excitation force on the direction of the spring's elongation and an operating moment at the supported point. A negative-velocity-feedback (NVF) controller is inserted into the main system to reduce the undesired vibrations that affect the system's efficiency, especially at the resonance state.
View Article and Find Full Text PDFSci Rep
October 2024
Department of Mathematics, Suresh Gyan Vihar University, Jaipur, Rajasthan, India.
J Mol Model
September 2024
Department of Physics, Presidency College, Chennai, Tamil Nadu, 600005, India.
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