SOS-based H∞ control of 2-D polynomial FMLSS model

1-D polynomial systems become more and more popular in respect that the systems are generalization of conventional 1-D linear systems and can represent nonlinear control systems effectively. Based on the same consideration, conventional 2-D Fornasini Marchesini local state space (FMLSS) models are extended to 2-D polynomial FMLSS model in this paper, with the elements of the system matrices are polynomial. The problems of stability analysis and H_∞ control for the 2-D polynomial FMLSS model are considered: a sufficient condition for stability of 2-D polynomial FMLSS model is proposed and a polynomial H_∞ controller is obtained in terms of sum of squares (SOS). An example is provided to show the effectiveness of the approach.