Efficient LMI Conditions for Enhanced Stabilization of Discrete-Time Takagi–Sugeno Models via Delayed Nonquadratic Lyapunov Functions

Pedro Henrique Coutinho (1) , Jimmy Lauber (2, 3) , Miguel Bernal (4) , Reinaldo Martinez Palhares (1)

1 UFMG - Universidade Federal de Minas Gerais = Federal University of Minas Gerais [Belo Horizonte, Brazil]
2 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
3 INSA Hauts-De-France - INSA Institut National des Sciences Appliquées Hauts-de-France
4 Electrical and Electronics Departement (Instituto Tecnológico de Sonora (ITSON))

This paper is concerned with the reduction of conservatism on stabilization conditions of discrete-time Takagi-Sugeno fuzzy models via delayed nonquadratic Lyapunov functions. A fruitful approach recently appeared in the literature, which, despite its benefits, dramatically increases the number of linear matrix inequalities needed to synthesize a controller. The two sets of sufficient conditions hereby proposed tackle this numerical problem while reducing conservatism and increasing the stabilization domain of existing conditions in literature, as illustrated in several examples.

Mots clés: "Delays"; "Lyapunov methods"; "Indexes"; "Linear matrix inequalities"; "Symmetric matrices"; "Takagi-Sugeno model"; "Numerical models"

Domaines: Automatique / Robotique

Pedro Henrique Coutinho, Jimmy Lauber, Miguel Bernal, Reinaldo Martinez Palhares. Efficient LMI Conditions for Enhanced Stabilization of Discrete-Time Takagi–Sugeno Models via Delayed Nonquadratic Lyapunov Functions. IEEE Transactions on Fuzzy Systems, 2019, 27 (9), pp.1833-1843. ⟨10.1109/TFUZZ.2019.2892341⟩. ⟨hal-03426282⟩