Robust control for nonhomogeneous Markov jump processes: an application to DC motor device

This paper studies the problem of robust H ∞ controller design for a class of uncertain Markov jump systems with time-varying transition probabilities, which follows nonhomogeneous jump processes. The time varying transition probability matrix is described as a polytope set. By Lyapunov function approach, under the designed controller, a sufficient condition is presented to ensure that the resulting closed-loop system is stochastically stable and that a prescribed H ∞ performance index is satisfied. Finally, an application of a DC motor device is addressed to demonstrate the effectiveness of developed techniques.