Extended state observer-based finite-region control for 2-D Markov jump systems

In this article, an extended state observer-based finite-region control scheme is presented for two-dimensional Markov jump systems with unknown mismatched disturbances. The mathematical model of the two-dimensional Markov jump systems is built on the well-known Roesser model. By establishing special recursive formulas and utilizing the 2-D Lyapunov function theory, sufficient conditions are obtained, which prove that the resultant system is finite-region bounded, if some linear matrix inequalities are achieved. Then, we provide an algorithm to solve the extended state observer-based controller gains. With the proposed control scheme, the external disturbances can be actively rejected from the system outputs. To conclude, a numerical example based on the Darboux equation is provided to demonstrate the validity and effectiveness of the devised control scheme.