On reference model tracking for Markov jump systems

Abstract

This article 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 ℋ_∞ control problem and an approach to synthesise the state feedback controller that quadratically stabilises the augmented dynamics and at the same time rejects the external disturbance that is developed. This approach is based on the solution of some linear matrix inequalities. A numerical example is provided to show the usefulness of the developed results.

Keywords:

• Markov jump systems
• stabilisation
• state feedback
• ℋ_∞ control
• linear matrix inequalities