We provide a small-gain theorem for feedback interconnections of monotone input-output systems with multi-valued input-state characteristics. This extends a small-gain theorem of Angeli and Sontag for monotone systems with singleton-valued characteristics. We prove our theorem using Thieme's convergence theory for asymptotically autonomous systems. We also provide an illustrative example. © 2006 IEEE.
Publication Source (Journal or Book title)
IEEE Transactions on Automatic Control
Malisoff, M., & De Leenheer, P. (2006). A small-gain theorem for motone systems with multivalued input-state characteristics. IEEE Transactions on Automatic Control, 51 (2), 287-292. https://doi.org/10.1109/TAC.2005.863534