A Lyapunov-Lurye Functional Parametrization of Discrete-Time Zames-Falb Multipliers

We consider the absolute stability of discrete-time Lurye systems with SISO/MIMO (non-repeated SISO) nonlinearities that are sector bounded and slope restricted. For this class systems, we present a parametrization Lyapunov-Lurye functional (LLF) is time-domain equivalence to finite impulse response (FIR) Zames-Falb multipliers. As searches over FIR multipliers provide best-known results in literature, here provides Lyapunov function for stability. A motivation alternative making it easy analyze system time domain, especially when frequency domain expression not straightforward. In letter, show between proposed LLF theoretically numerically.