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l∞ Fuzzy Filter Design for Nonlinear Systems with Missing Measurements: Fuzzy Basis-dependent Lyapunov Function Approach

Sun Young Noh, Geun Bum Koo, Jin Bae Park*, and Young Hoon Joo
International Journal of Control, Automation, and Systems, vol. 14, no. 2, pp.425-434, 2016

Abstract : In this paper, l∞ fuzzy filtering problem is dealt for nonlinear systems with both persistent bounded disturbances and missing probabilistic sensor information. The Takagi–Sugeno (T–S) fuzzy model is adopted to represent a nonlinear dynamic system. The measurement output is assumed to contain randomly missing data, which is modeled by a Bernoulli distributed with a known conditional probability. To design the l∞ fuzzy filter and guarantee tracking performance, the effect of the perturbation against persistent bounded disturbances is reduced by using the minimum l∞ performance. By using the fuzzy basis-dependent Lyapunov function approach, a sufficient condition is established that ensure the mean square exponential stability of the filtering error. The proposed sufficient condition is represented as some linear matrix inequalities (LMIs), and the filter gain is obtained by the solution to a set of LMIs. Finally, the effectiveness of the proposed design method is shown via an example.

Keyword : l∞ fuzzy filter, missing measurements, Takagi-Sugeno fuzzy model, fuzzy basis-dependent Lyapunov function, linear matrix inequalities.

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