Rate of convergence to periodic regimes in nonlinear feedback systems with strongly convex backlash characteristics
Year: 2025
Type: article
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.
Source: Mathematics in Engineering
DOI: 10.3934/mine.2025025
Authors: Igor G. Vladimirov, Ian R. Petersen
Institution: Australian National University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414412878