On Discrete-Time Partial Averaging

The majority of literature for partial averaging techniques for discrete-time systems has focused on showing the local exponential stability properties of nonlinear time-varying systems when the partial averaged system is uniformly locally exponential stable. The work generalizes the existing partial averaging techniques to a more general class of systems in which the partial averaged system is uniformly globally asymptotically stable (UGAS). By using closeness of solutions (Proposition 1) between the original system and the partial averaged system, the main result shows that the original time-varying system will be semi-globally practically asymptotically (SPA) stable provided that the partial averaged systems is UGAS and the tuning parameters are sufficiently small. A few other stability results of the original system from different stability properties of its partial averaged system are also presented. Simulation results support our theoretical findings.