Decentralized $H_\infty$ Sampled-Data Fuzzy Filter for Nonlinear Interconnected Oscillating Systems With Uncertain Interconnections

This paper proposes a decentralized $H_\infty$ sampled-data fuzzy filter design for nonlinear interconnected systems composed of multiple subsystems with uncertain interconnections and variable sampling intervals. The interconnected system and the decentralized filter are modeled using Takagi–Sugeno fuzzy systems. To derive the filter-design conditions, the estimation error dynamics are modeled, and the $H_\infty$ filter performance inequality is defined. The filter performance inequality is aimed at minimizing the ratio of the estimation error to the sum of the norm of the disturbance and oscillating system. The sufficient conditions for the filter design are derived using the Wirtinger-based integral inequality and expressed in the form of linear matrix inequalities. Finally, the performance of the proposed filter-design techniques is demonstrated through two simulation examples.