L _∞ fuzzy filter for non‐linear systems with intermittent measurement and persistent bounded disturbances

Abstract

This study is concerned with an L ∞ filtering problem for non-linear systems with persistent bounded disturbances and intermittent measurements. The non-linear plant is represented by the Takagi-Sugeno (T-S) fuzzy model that is employed to approximate the non-linear dynamic systems. The system measurements may be unavailable at any sample time and the probability of the occurrence of missing data is assumed to be known. In this study, to design the L ∞ fuzzy filter with the estimation error, the estimation error because of persistent bounded disturbance is minimised by some linear matrix inequalities and the filter error system is stochastically stable in the mean square. A stochastic variable satisfying the Bernoulli random binary distribution is utilised to model the phenomenon of the missing data. Finally, the results indicate that the proposed method attenuates the peak of estimation error and preserves a guaranteed L ∞ -gain performance.