By correlating the geometric sequence of numbers a, a2, a3,…(a is called the base) and the arithmetic sequence 1, 2, 3,…and interpolating to fractional values, it is possible to reduce the problem of multiplication and division to one of addition and subtraction.
By introducing the geometric sequence division (GSD) method, the discrete delay interval can be separated into multiple subintervals with unequal lengths based on the common ratio α.
In this paper, by introducing the geometric sequence division and integral delay partitioning approaches, stability problems of the perturbed T-S fuzzy systems with mixed delays are investigated.
The first and the second solutions are respectively given by the arithmetic and the geometric sequences.
The resulting geometric sequence therefore yielded a dense set of values, suitable for constructing a table.
Although a grid-search way can be employed to seek 'optimal' C parameters by trying a geometric sequence such as 2−10,2−9,…2,…2 under a specified cross validation for each data set [ 13], such an approach may not contribute to generalizable diagnostic results and possible prohibitive training time demand.
By using the summation of geometric sequence, (6) is changed to be R k = ∑ m = 0 N − 1 A m 1 − e j 2 π m T r − k T s / T s 1 − e j 2 π m T r − k T s / N T s e − j 2 πmt / N T s + η ″ (7).
We further simplified this model by approximating the three weights w i with a geometric sequence with the common ratio α.
The setup for the rest of the grid hierarchy is calculated using a geometric sequence for grid spacing.
