Hybrid Descriptor System State Estimation through an IMM Approach**This work has been supported by the ITEA2 MODRIO project.

Stochastic hybrid systems have been largely studied in the literature in the framework of Markov mode transitions and linear Gaussian state space mode models. In order to generalize such results to hybrid systems involving phenomena characterized by difierential- algebraic equations, this paper studies the problem of state estimation for stochastic hybrid systems with modes described by descriptor equations. The proposed state estimation algorithm follows the interacting multiple model (IMM for short) approach, but the classical state space system Kalman filters are replaced by descriptor system Kalman filters. Because of the dificulty for computing the innovation of each descriptor system Kalman filter, a new method for likelihood evaluation is proposed, as one important step of the new IMM algorithm. Numerical examples are presented to illustrate the performance of the proposed algorithm.