Abstract
In this paper, we propose an efficient relaxation method of the parameterized linear matrix inequalities (PLMIs) in the framework of the state-feedback stabilization problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems. The matrix elimination method plays a key role in deriving the criterion, which reduces the order of the fuzzy weights by eliminating the quadratic fuzzy weights in the original PLMIs and then transformed to a more tractable one. A partition on the range of the fuzzy weights is introduced, through which a linearly weight-dependent condition can be developed by fixing some decision variables piecewisely. By utilizing the extreme points of each partition, the negativity of the condition can be guaranteed and the corresponding controller is represented in the form of a switching control law based on the partition. Some example shows that finer subdivision in the partition leads to a better performance behavior.
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