Controllability and Observability of Piecewise Impulsive Systems on Arbitrary Time Domains

In this paper, by employing the time scales theory, we establish the necessary and sufficient conditions for the controllability and observability of piecewise impulsive dynamic systems on arbitrary time domains. We constructed a piecewise control function which controls the system not only at the final time of the intervals but also at every impulse point, i.e., we investigate the so-called total controllability results. In this study, we mainly use the Gramian type matrices, variation of parameter formula, and time scales theory. We give some simulated results for different time domains to validate the theoretical results. Furthermore, we provide an application of these results to the population dynamics. The obtained results are non-trivial and new, extending and generalising the existing ones.