Strict Lyapunov Functions for the Super-Twisting Consensus Algorithm

The super-twisting algorithm is widely used in the design of controllers, observers, and differentiators. This paper investigates its application to achieve consensus among a team of peer agents characterized by first-order perturbed dynamics. Agents communicate through a directed, weight-balanced communication topology. The key contributions include employing the super-twisting algorithm to solve the finite-time robust consensus problem and developing a method for constructing a family of strict Lyapunov functions to analyze its robust stability. The analysis is based on the Lyapunov approach, and the necessary conditions for the stability of the closed-loop system are derived. Simulations supporting the theoretical analysis are also provided.