Strict Passivity Criterion for Lipschitz Nonlinear Discrete-Time System with Saturation Overflow Arithmetic

This article examines the stability behavior of Lipschitz nonlinear discrete-time systems employing saturation overflow and external disturbance. The proposed criterion utilizes a very strict passivity-based approach for stability investigation of the interfered discrete-time systems. A novel stability criterion for the externally interfered nonlinear discrete-time system is established using the quadratic Lyapunov function, saturation characteristics, and Lipschitz condition. The derived criterion assures the passivity performance for the given discrete-time system in terms of its storage function. The presented criterion confirms the asymptotic stability in the presence of zero external disturbance and eliminates the overflow oscillations in a discrete-time system. The obtained conditions are represented in linear matrix inequality for easy tractability. The practicality of the proposed work is verified through numerical examples.