Tight Bounds for Averaging Multi-Frequency Differential Inclusions, Applied to Control Systems

Abstract

Abstract. We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of order O (ǫ) on the approximation error. These results are then applied to control systems consisting of a sum of time-periodic functions.