Finite and fixed‐time stabilization of discrete‐time systems using passivity‐based control

In this paper, we propose a new passivity‐based controller design technique for discrete‐time fully actuated systems. The controller establishes finite‐time and fixed‐time convergence of dynamical system trajectories to an equilibrium state. A new form of a dissipation function, selected a priori, is introduced to design a feedback control rule to achieve such convergence properties. An energy shaping and damping injection methodology is extended to achieve non‐asymptotic stabilization. A numerical example to validate the proposed methods is provided.