2024/06/21 by Chris Guiver, Guiver, Chris
Engineering · Mathematics · #34A12 #34A60 #34C27 #34D20 #93C10 #93C35 #93D09 #93D15 #Classical Analysis and ODEs (math.CA) #Control and Stability of Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2406.15099
openalex publication_date 2024/06/21 · openalex created_date 2024/06/25 · openalex updated_date 2026/07/28
A suite of input-to-state stability results are presented for a class of forced differential inclusions, so-called Lur'e inclusions. As a consequence, semi-global incremental input-to-state stability results for systems of forced Lur'e differential equations are derived. The results are in the spirit of the passivity theorem from control theory as both the linear and nonlinear components of the Lur'e inclusion (or equation) are assumed to satisfy passivity-type conditions. These results provide a basis for the analysis of forced Lur'e differential equations subject to (almost) periodic forcing terms and, roughly speaking, ensure the existence and attractivity of (almost) periodic state- and output-responses, comprising another focus of the present work. One ultimate aim of the study is to provide a robust and rigorous theoretical foundation for a well-defined and tractable ``frequency response'' of forced Lur'e systems.