Abstract
In this brief paper, the problem of H ∞ fuzzy filtering design is further studied and two cases (Case A: the premise variables are known and Case B: the premise variables are unknown) are considered. Different from all the filtering design methods in the literature, in this paper, the time derivatives of the membership functions involved in the Lyapunov function are dealt with by a switching method. Then, for different cases of the premise variables, different switching filters are designed and the membership function dependent Lyapunov function is applied to derive some LMIs (linear matrix inequalities). Furthermore, some discussions on how to further relax the results by applying the polynomial membership functions dependent matrices or by introducing more free variables are given in two remarks. In the end, two numerical examples are given to show the effectiveness of the proposed approach.
Highlights
INTRODUCTIONAs the development of artificial intelligence, there are lots of results about fuzzy systems such as [1]–[9] (see [10] and the references therein) among which, filtering design is a hot topic
In recent years, as the development of artificial intelligence, there are lots of results about fuzzy systems such as [1]–[9] among which, filtering design is a hot topic
The problem of designing non-fragile H∞ filter with D stability constraints is studied in [12] where the filter to be designed is assumed to be with multiplicative gain variations and a sufficient condition for the nonfragile H∞ filter design is proposed in terms of LMIs
Summary
As the development of artificial intelligence, there are lots of results about fuzzy systems such as [1]–[9] (see [10] and the references therein) among which, filtering design is a hot topic. The problem of designing non-fragile H∞ filter with D stability constraints is studied in [12] where the filter to be designed is assumed to be with multiplicative gain variations and a sufficient condition for the nonfragile H∞ filter design is proposed in terms of LMIs. The filter design with time-delay is considered, for example, the problem of fuzzy robust L2 − L∞ filtering for a class of delayed T-S fuzzy systems is investigated in [13] where the Lyapunov function is dependent on the membership function and the results are presented as linea matrix inequalities but the time derivatives of membership function are supposed to be bounded. Almost at the same time, new results about designing H∞ fuzzy filters with time-varying delay are obtained in [15] by estimating the upper bounds of the derivatives of Lyapunov functionals without ignoring some useful terms. Two examples (One is for case A and other is for case B) are provided to verify the conclusions given in this paper
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