Publication
A practical test for assessing the reachability of discrete-time Takagi-Sugeno fuzzy systems
Journal Article (2015)
Journal
Journal of the Franklin Institute
Pages
5936–5951
Volume
352
Number
12
Doc link
http://dx.doi.org/10.1016/j.jfranklin.2015.10.006
File
Abstract
This paper provides a necessary and sufficient condition for the reachability of discrete-time Takagi–Sugeno fuzzy systems that is easy to apply, such that it constitutes a practical test. The proposed procedure is based on checking if all the principal minors associated to an appropriate matrix are positive. If this condition holds, then the rank of the reachability matrix associated to the Takagi–Sugeno fuzzy system is full for any possible sequence of premise variables, and thus the system is completely state reachable. On the other hand, if the principal minors are not positive, the property of the matrix being a block P one with respect to a particular partition of a set of integers is studied in order to conclude about the reachability of the Takagi–Sugeno system. Examples obtained using an inverted pendulum are used to show that it is easy to check this condition, such that the reachability analysis can be performed efficiently using the proposed approach.
Categories
fuzzy control.
Scientific reference
M. Witczakc, D. Rotondo, V. Puig and P. Witczakc. A practical test for assessing the reachability of discrete-time Takagi-Sugeno fuzzy systems. Journal of the Franklin Institute, 352(12): 5936–5951, 2015.
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