Contractivity Analysis and Control Design for Lur'e Systems: Lipschitz, Incrementally Sector Bounded, and Monotone Nonlinearities

Abstract: In this paper, we study the contractivity of Lur'e dynamical systems whose nonlinearity is either Lipschitz, incrementally sector bounded, or monotone. We consider both the discrete- and continuous-time settings. In each case, we provide state-independent linear matrix inequalities (LMIs) which are necessary and sufficient for contractivity. Additionally, we provide LMIs for the design of controller gains such that the closed-loop system is contracting. Finally, we provide a numerical example for control design.