Groupe d’études et de recherche en analyse des décisions

# On Filtering for Singular Linear Systems with Random Abrupt Changes

## El-Kébir Boukas

This paper deals with the class of continuous-time singular linear Markovian jump systems with totally and partially known transition jump rates. The filtering problem of this class of systems is tackled. New sufficient conditions for $\cal{H}_\infty$ filtering are developed. A design procedure for the $\cal{H}_\infty$ filter which guarantees that the dynamics of the filter error will be piecewise regular, impulse-free and stochastically stable with $\gamma$-disturbance rejection is proposed. It is shown that the addressed problem can be solved if the corresponding developed linear matrix inequalities (LMIs) with some constraints are feasible. A numerical example is employed to show the usefulness of the proposed results.

, 24 pages