Therecently 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 anykκk2 are also solvable.
Bibliographical noteFunding Information:
Manuscript received May 21, 2010; revised September 23, 2010; accepted December 6, 2010. Date of publication December 23, 2010; date of current version June 6, 2011. This work was supported in part by the National Research Foundation of Korea Grant funded by the Korean Government under Grant KRF-2009-220-D00034.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computational Theory and Mathematics
- Artificial Intelligence
- Applied Mathematics