Global Asymptotic Stability Certificates for Discrete-Time Lur'e Systems under Incremental-like Restrictions

In this paper, we provide Lyapunov-based conditions for assessing the global asymptotic stability of nonlinear discrete-time Lur'e systems under incremental-like restrictions. The proposed results invoke dissipation arguments for the linear and nonlinear components of the dynamics and rely on a Lyapunov function with a few parameters and integral terms. The proof of the main result does not require any approximations of the integral terms. The impact of the result is highlighted through a comparison with the literature.