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Further Theoretical Justification of the k -Samples Variation Approach for Discrete-Time Takagi–Sugeno Fuzzy Systems

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3 Author(s)
Dong Hwan Lee ; Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea ; Jin Bae Park ; Young Hoon Joo

The recently developed k-samples variation approach is known as a powerful way to reduce the conservativeness of existing stability and stabilization conditions for discrete-time Takagi-Sugeno (T-S) fuzzy systems. In this approach, the Lyapunov functions under consideration are not necessarily decreasing at every sample but are allowed to decrease every k samples, which is evidently less restrictive than classical approaches. Consequently, less-conservative linear-matrix-inequality (LMI) conditions were derived. In addition, it was proved that, for two positive integers k1 and k2, if the condition for k=k1 is fulfilled, then those corresponding to k=k2 are also satisfied when k2 is the divisor of k1. In this letter, we prove that, if the condition for k=k2 admits a solution, then those corresponding to any k >; k2 are also solvable.

Published in:

IEEE Transactions on Fuzzy Systems  (Volume:19 ,  Issue: 3 )