Asymptotic behavior of infinite systems determined by polynomial shift operators

Abstract

This paper studies the asymptotic behavior of infinite dimensional systems determined by polynomial shift operators. The results from ergodic theory and C0‐semigroups are used to obtain a characterization of those initial states which lead to convergent solutions. Estimates on the rate of convergence for solutions are obtained under a stronger ergodic condition on corresponding initial states. The results can be used to solve the robot rendezvous problem and investigate platoon systems.