Filtering of T–S Fuzzy Systems With Nonuniform Sampling

The problem of asynchronous filtering of nonlinear systems is investigated in this paper. To facilitate analysis, a discrete-time Takagi-Sugeno fuzzy model with a fast and uniform period is introduced to approximate continuous nonlinear systems. A slow and nonuniform sampler between system and filter is proposed to overcome the contradictions between fast sampling period and limited bandwidth. The nonuniform sampling interval of sampler is subject to a Markov chain. To make full use of the partial information of sampling interval which is accessible to the filter, the asynchronous filter which is described by the hidden Markov model is introduced to reduce conservatism. By resorting to the augmentation approach and the Lyapunov functional method which depends on nonuniform sampling interval, some sufficient conditions for the existence of asynchronous filer are given to guarantee the stability and dissipativity of the augmented system. The gains of asynchronous filter are given via solving a set of linear matrix inequalities. Two examples are utilized to illustrate the validity of the developed filter design technique where the relationships between optimal dissipative performance indices and the mode synchronization rate are given.