Contact Name: Prof. Lorenzo Marconi
Abstract
Very few results exist in the literature concerning the definition of observability or the design of observers for hybrid systems. This is mainly due to the fact that those systems combine both continuous and discrete behaviors, and their trajectories have different time domains, which makes it hard to compare them. In this seminar, we start by considering the favorable case where the jump times of the solutions are supposed to be known and propose sufficient conditions for observer design when the flow/jump maps are linear. Those conditions take the form of matrix inequalities, which cover cases where the time between successive jumps is unbounded or tends to zero (Zeno behavior), and cases where either both the continuous and discrete dynamics, only one of them, or none of them are detectable. In a second part, we attempt to define detectability and observers in the general case where the jump times are unknown. We explain the problems that those definitions raise, and how they can be resolved by re-parameterizing the jumps of the solutions to bring them on a same domain.