A Less Conservative LMI Condition for Stability of Discrete-Time Systems with Slope-Restricted Nonlinearities

摘要

Many conditions have been found for the absolute stability of discrete-time Lur’e systems in the literature. It is advantageous to find convex searches via LMIs where possible. In this technical note, we construct two less conservative LMI conditions for discrete-time systems with slope-restricted nonlinearities. The first condition is derived via Lyapunov theory while the second is derived via the theory of integral quadratic constraints (IQCs) and noncausal Zames–Falb multipliers. Both conditions are related to the Jury–Lee criterion most appropriate for systems with such nonlinearities, and the second generalizes it. Numerical examples demonstrate a significant reduction in conservatism over competing approaches.