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

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dc.contributor	Universitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial
dc.contributor	Universitat Politècnica de Catalunya. SIC - Sistemes Intel·ligents de Control
dc.contributor	Universitat Politècnica de Catalunya. SAC - Sistemes Avançats de Control
dc.contributor.author	Witczak, Marcin
dc.contributor.author	Rotondo, Damiano
dc.contributor.author	Puig Cayuela, Vicenç
dc.contributor.author	Witczak, Piotr
dc.date	2015-12-01
dc.identifier.citation	Witczak, M., Rotondo, D., Puig, V., Witczak, P. A practical test for assessing the reachability of discrete-time Takagi-Sugeno fuzzy systems. "Journal of the Franklin Institute", 01 Desembre 2015, vol. 352, núm. 12, p. 5936-5951.
dc.identifier.citation	0016-0032
dc.identifier.citation	10.1016/j.jfranklin.2015.10.006
dc.identifier.uri	http://hdl.handle.net/2117/83682
dc.language.iso	eng
dc.relation	http://www.sciencedirect.com/science/article/pii/S0016003215003804
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Informàtica::Automàtica i control
dc.subject	Takagi-Sugeno model
dc.subject	Fuzzy systems--Mathematical models
dc.subject	SWITCHED LINEAR-SYSTEMS
dc.subject	NONLINEAR STOCHASTIC-SYSTEMS
dc.subject	BANACH-SPACES
dc.subject	CONSTRAINED CONTROLLABILITY
dc.subject	MATRICES
dc.subject	DESIGN
dc.subject	DELAYS
dc.subject	SETS
dc.subject	Sistemes borrosos -- Models matemàtics
dc.title	A practical test for assessing the reachability of discrete-time Takagi-Sugeno fuzzy systems
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.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 teachability analysis can be performed efficiently using the proposed approach.
dc.description.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 teachability analysis can be performed efficiently using the proposed approach.

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