A Novel Criterion for Realizing H∞ Overflow Oscillation-Free Digital Filters with Saturation and External Interference
摘要
Fixed-point digital filters (DFs) implemented on finite wordlength processors (such as microcontrollers, Field-programmable Gate Arrays, and digital signal processing kits) often experience nonlinearities due to quantization and overflow, which can lead to instability. In practice, the stability of DFs affected by external interference and saturation overflow nonlinearities is a crucial concern. This paper presents a novel criterion for realizing H∞ overflow oscillation-free DFs with saturation and external interference, wherein overflow correction takes place after the summation of coefficient product terms and interference. The criterion is based on an improved lemma that utilizes more detailed system information to characterize saturation nonlinearities more accurately. In addition to guaranteeing the exponential stability of the DF, the criterion can be used to mitigate the effects of interference to meet an H∞ norm constraint. To achieve the minimal H∞ performance for a specific DF, a convex optimization problem is formulated with linear matrix inequality constraints. Two examples are provided to demonstrate the usefulness of the proposed criterion. The criterion is shown to yield H∞ stability results that are not covered by several existing methods.