Abstract
This brief investigates the problem of relaxed observer-based multi-instant fuzzy state estimation of discrete-time nonlinear circuits. In contrast with the recent result whose observer gain matrices may be too many to be applied in practice, there is only an unique group of observer gain matrices required in this study while the conservatism can be reduced markedly by developing a new slack variables technique. The proposed slack variables technique is constructed on the basis of multi-instant homogenous polynomials so that much more recessive algebraic properties of the normalized fuzzy weighting functions can be excavated in order to remove those redundant positive definite constraints which bring about conservatism. Especially, those previous slack variables techniques belong to special cases of ours. Finally, a benchmark example is given to validate the progressiveness of the developed result.
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