Finite-Time Input to State Stability of Discontinuous Dynamical Systems: A Case Study of Networked Euler-Lagrange Systems

In this study, Finite-Time Input-to-State Stability (FTISS) is considered for discontinuous dynamical systems based on extended Filippov's solutions and non-smooth Lyapunov functions. The convergence of these systems is analyzed using non-smooth and set-valued analysis, thereby proving the existence of a finite-time input-to-state Lyapunov function for the intended systems implies FTISS of these systems. As an illustration, the results of the theorem are applied to study finite-time input-to-state stability of Multi-Agent Systems (MASs) with Euler-Lagrange dynamics.