A practical test for assessing the reachability of discrete-time Takagi-Sugeno fuzzy systems

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.

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