Finite/fixed-time synchronized stability of autonomous discrete-time dynamical systems

This study reports the finite/fixed-time synchronized stability of autonomous discrete-time dynamical systems. The specific objective is to ensure simultaneous convergence of all system states to the equilibrium point and remain there thereafter. The novel Lyapunov and converse Lyapunov theorems are introduced to analyze the finite/fixed-time stability of three distinct discrete-time systems. Additionally, we propose the use of generalized p-norm on finite-dimensional vector spaces, which is based on the function of scaled p-norm that we previously proposed. This can be utilized in dynamical systems to accelerate the convergence rate of the system. Finally, numerical simulations show the effectiveness of finite/fixed-time synchronized stability, and the advantages of utilizing the scaled p-norm in fast convergence.