Reachability and Observability of Periodic Descriptor Systems

In the second-half of the last century, the development of systems and control theory, together with the achievements of digital control and signal processing, has set the stage for renewed interest in the study of periodic systems, both in continuous and discrete time; see, e.g., [24, 45, 36, 10, 43, 12] and the survey papers [3, 4]. This has been amplified by specific application demands in the aerospace realm [17, 25, 16], computer control of industrial processes [5] and communication systems [35, 10, 34, 44]. The number of contributions on linear time-varying discrete-time periodic systems has been increasing in recent times; see, e.g., [13, 15, 18, 37, 39, 40] and the references therein. This increasing interest in periodic systems has also been motivated by the large variety of processes that can be modelled through linear discrete-time periodic systems (e.g., multirate sampled-data systems, chemical processes, periodically time-varying filters and networks, and seasonal phenomena [2, 3, 7, 14, 23, 26, 42]). We consider here a periodic time-varying descriptor system of the form