Total controllability of positive switched dynamic systems with non-instantaneous impulses using non-uniform time domains

Abstract This study explores total controllability in dynamic systems where maintaining positivity is crucial. While traditional models demand positive inputs, our work introduces the concept of positive state total controllability, offering a more adaptable perspective, particularly beneficial in population biology. We establish a key connection between positive state total controllability and positive input total controllability, by considering Kalman-like criteria. By using time scales theory, we extend our analysis to linear positive switched systems with non-instantaneous impulses, providing unified and extended results across various time domains. The proposed theory is validated through both theoretical insights and numerical examples. This research not only enhances our understanding of control theory but also encourages further exploration in this evolving domain.