Abstract
In this paper, a robust mixed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_2/H_infty$</tex> filtering problem for continuous-time fuzzy systems subject to parameter uncertainties and multiple time-varying delays in state variables is addressed. The uncertain systems are expressed as Takagi–Sugeno fuzzy models with linear nominal parts and norm-bounded uncertainties. The main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_infty$</tex> performance under worst case disturbance. Based on Lyapunov theory, both delay-independent and delay-dependent sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of linear matrix inequalities. Therefore, stable filters can be obtained easily with existing convex algorithms. Lastly, two examples are given to illustrate the proposed design methodology.
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