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.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computational Theory and Mathematics
- Artificial Intelligence
- Applied Mathematics