Input-to-state Stability for Hybrid Kalman Filters

Abstract

In this article, we propose a Lyapunov-based characterization of exponential input-to-state stability (ISS) for hybrid systems. We propose a new formulation of the continuous-discrete Kalman filter algorithm Särkkä (2006) using the hybrid systems framework Goebel et al. (2012) where we consider continuous-time system dynamics and discrete-time observations. We prove exponential input-to-state stability on the estimation error of the hybrid Kalman filter under mild assumptions on the system's model.