The September 2017 solar flares and the subsequent geomagnetic storms driven by the coronal mass ejections were recognized as the ones of the most powerful space weather events during the current solar cycle. The occurrence of the most powerful solar flares and magnetic storms during the declining phase of a solar cycle is a common phenomenon, and the current cycle is no exception. Nowadays, thorough and multifactor space weather monitoring is required to prevent the damages from the destructive space weather impact on the technological systems on the Earth. The purpose of this study is to better characterize these events by applying the generalized characteristic function approach for combined analysis of geomagnetic activity indices, total electron content data and secondary cosmic ray data from the muon hodoscope that contained Forbush decreases resulting from solar plasma impacts. A combined analysis of secondary cosmic ray data from the muon hodoscope, geomagnetic activity indices and total electron content data is presented. The main advantage of this approach is the possibility to identify low-amplitude specific features in datasets characterizing several environmental sources. As an example, different datasets available over the storm period 6-11 September 2017 were analyzed in a unified way. The new developed technique allows us to study various space weather effects and obtain new mutually supportive information on different phases of storm evolution, based on the geomagnetic and other environmental observations in the near-Earth space.