In this paper we address the problem of extracting dynamics from multi-dimensional time-evolving data. To this end, we propose a linear dynamical model (LDS), which is based on the higher order decomposition of the observation data. In this way, we are able to extract a new descriptor for analyzing data of multiple elements coming from of the same or different data sources. Each sequence of data is modeled as a collection of higher order LDS descriptors (h-LDSs), which are estimated in equally sized temporal segments of data. Finally, each sequence is represented as a term frequency histogram following a bag-ofsystems approach, in which h-LDSs are used as feature descriptors. For evaluating the performance of the proposed methodology to extract dynamics from time evolving multidimensional data and using them for classification purposes in various applications, in this paper we consider two different cases: dynamic texture analysis and human motion recognition. Experimental results with two datasets for dynamic texture analysis and two datasets for human action recognition demonstrate the great potential of the proposed method.