Groupe d’études et de recherche en analyse des décisions

# On Reference Model Tracking for Markov Jump Systems

## El-Kébir Boukas

This papers deals with the tracking problem for the Markov Jump systems with external finite energy disturbance. A state feedback controller that makes the state vector of the system track precisely a given state vector of a reference model is proposed. The tracking problem is formulated as an $\cal{H}_\infty$ control problem and an approach to synthesize the state feedback controller that quadratically stabilizes the augmented dynamics and at the same time rejects the external disturbance is developed. This approach is based on the solution of some linear matrix inequalities (LMIs). A numerical example is provided to show the usefulness of the developed results.

, 21 pages