Stability of Discrete‐Time Stochastic Systems With Path Information and Applications

ABSTRACT This paper investigates the stability of discrete‐time stochastic systems with path information and its application to the distributed protocol design for discrete‐time stochastic multi‐agent systems. First, for discrete‐time stochastic systems incorporating integral and fragment‐integral path information, novel mean‐square and almost sure exponential stability criteria are established, respectively. The analysis reveals that the inclusion of discrete fragment‐integral information contributes to enhanced stochastic stability. Based on the proposed stability criteria, the distributed consensus problem for discrete‐time stochastic multi‐agent systems is further explored under a path information feedback framework. Specifically, discrete proportional‐integral and proportional‐fragment‐integral consensus protocols are designed and sufficient conditions for achieving mean‐square and almost sure consensus are derived, indicating that the discrete fragment‐integral term can facilitate consensus performance in stochastic environments. Motivated by this consensus‐enhancing capability, the proportional‐fragment‐integral protocol is further adopted, and a corresponding algorithm is developed for discrete‐time automated vehicle systems to achieve platoon control objectives. Finally, numerical simulations are provided to validate the theoretical results.