Decentralized State Feedback Control of Uncertain Affine Fuzzy Large-Scale Systems With Unknown Interconnections

This paper investigates the problem of the decentralized state feedback controller design for a class of nonlinear large-scale systems described by uncertain affine fuzzy models with unknown interconnections. First, based on the structural information encoded in the fuzzy rules, the affine fuzzy large-scale system is represented by multiple operating-regime-based models. Then, a decentralized state feedback controller is designed, and a cyclic-small-gain condition is introduced to address the unknown interconnections, such that the resulting closed-loop system is asymptotically stable with the disturbance attenuation. By constructing a piecewise Lyapunov function combined with S-procedure and adding slack matrix variables, a convex decentralized controller design condition is derived in the formulation of linear matrix inequalities, where the system matrix is separated from Lyapunov matrix, such that the controller parameterization is independent of the Lyapunov matrix. In contrast with the existing results, the derived stabilizability condition loosens restrictions on the decentralized controller design, and can be applied to handle the nonlinear large-scale systems without satisfying the matching condition. Finally, an example is given to illustrate the effectiveness and superiority of the new results.