Interval Observers for Hybrid Dynamical Systems with Known Jump Times

This paper proposes a novel asymptotically stable interval estimator design for hybrid systems with nonlinear dynamics and observations under the assumption of known jump times. The proposed architecture leverages the concepts of mixed-monotone decompositions to construct a hybrid interval observer that is guaranteed to frame the true states (i.e., is correct) by construction. Moreover, using Lyapunov analysis and the positive system property of the framer error dynamics, we propose two approaches for computing the observer gains to achieve asymptotic stability of the error system based on mixed-integer semidefinite and linear programs. Further, our observer design incorporates additional degrees of freedom that may provide some advantages similar to coordinate transformations. Finally, we demonstrate the efficacy of the proposed hybrid observer design using two illustrative examples.