Observer Design for Hybrid Systems with Linear Maps and Known Jump Times

International audience ; This chapter unifies and develops recent developments in observer design for hybrid systems with linear dynamics and output maps, whose jump times are known. We define and analyze the (pre-)asymptotic detectability and uniform complete observability of this class of systems, then present two different routes for observer design. The first one relies on a synchronized Kalman-like observer that gathers observability from both flows and jumps. The second one consists in decomposing the state into parts with different observability properties and coupling observers estimating each of these parts, possibly exploiting an extra fictitious measurement coming from the combination of flows and jumps. These observers are based on a Linear Matrix Inequality (LMI) or the Kazantzis-Kravaris/Luenberger (KKL) paradigm. A comparison of these methods is presented in a table at the end.