@article{Vladimirov2025, 
author = {Igor G. Vladimirov and Ian R. Petersen},
title = {Rate of convergence to periodic regimes in nonlinear feedback systems with strongly convex backlash characteristics},
year = {2025},
journal = {Mathematics in Engineering},
volume = {7},
number = {5},
pages = {610-636},
keywords = {backlash dynamics, strong convexity, dissipation inequality, periodic regime, Lyapunov exponent},
url = {https://www.sciopen.com/article/10.3934/mine.2025025},
doi = {10.3934/mine.2025025},
abstract = {This paper considers a class of hysteresis systems consisting of a linear part with an external input and feedback with a backlash nonlinearity. Assuming that the latter is specified by a strongly convex set, we establish estimates for the Lyapunov exponents which quantify the rate of convergence of the system state trajectories to a forced periodic regime when the input is a periodic function of time with a sufficiently large "amplitude". These results employ enhanced dissipation inequalities, arising from differential inclusions with strongly convex sets which were used previously for the Moreau sweeping process.}
}