Generalized non-monotonic Lyapunov functions for analysis and synthesis of Takagi-Sugeno fuzzy systems

Article type: Research Article

Authors: Coutinho, Pedro H.S.^a | Peixoto, Márcia L.C.^a | Lacerda, Márcio J. ^b | Bernal, Miguel^c | Palhares, Reinaldo M.^{d; *}

Affiliations: [a] Federal University of Minas Gerais, Graduate Program in Electrical Engineering, Brazil | [b] Department of Electrical Engineering, Federal University of São João del-Rei, Brazil | [c] Departament of Electrical and Electronics Engineering, Sonora Institute of Technology, Ciudad Obregón 85000, Mexico | [d] Department of Electronics Engineering, Federal University of Minas Gerais, Brazil

Correspondence: [*] Corresponding author. Reinaldo M. Palhares, Department of Electronics Engineering, Federal University of Minas Gerais, Brazil. E-mail: rpalhares@ufmg.br.

Abstract: This paper presents new stability and stabilisation conditions in the form of linear matrix inequalities for discrete-time Takagi-Sugeno fuzzy systems; they are derived considering a class of non-quadratic Lyapunov functions with multi-parametric non-monotonic terms, which significantly enhances the feasibility set of current state-of-the-art results. In addition, extensions to cope with the disturbance attenuation control problem are included. Benchmark numerical examples are provided to illustrate the effectiveness of the proposed approach.

Keywords: Stability analysis, control design, Linear Matrix Inequality, non-quadratic Lyapunov function, non-monotonic functions

DOI: 10.3233/JIFS-200262

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 3, pp. 4147-4158, 2020