Robust mixedH2/H∞filtering for discrete-time delay fuzzy systems

A robust mixed H 2/H∞ filtering problem for discrete-time fuzzy systems subject to parameter uncertainties and multiple time-varying delays in state variables is addressed in this paper. The uncertain systems are expressed as Takagi-Sugeno fuzzy models with linear nominal parts and norm-bounded uncertainties. The main objective is to design a stable filter which minimizes a guaranteed cost index and achieves a prescribed H∞ performance under worst-case disturbance. Based on Lyapunov theory, sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of LMIs. Therefore, stable filters are obtained with existing convex algorithms. Lastly, two examples are given to illustrate the proposed design methodology.