LMI-based control synthesis of constrained Takagi–Sugeno fuzzy systems subject to L2 or L∞ disturbances

• Published in: Neurocomputing (Amsterdam) Vol. 207; pp. 793 - 804
• Main Authors: Nguyen, Anh-Tu, Laurain, Thomas, Palhares, Reinaldo, Lauber, Jimmy, Sentouh, Chouki, Popieul, Jean-Christophe
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 26.09.2016
• Subjects: Control input saturation; Domain of attraction; Fuzzy Lyapunov functions; Non-parallel distributed compensation control scheme; Takagi–Sugeno fuzzy systems; Non-parallel distributed compensation control scheme; Fuzzy Lyapunov functions; Domain of attraction; Control input saturation; Takagi–Sugeno fuzzy systems
• ISSN: 0925-2312; 1872-8286
• DOI: 10.1016/j.neucom.2016.05.063

This paper is devoted to the development of a new saturated non-parallel distributed compensation control law for disturbed Takagi–Sugeno fuzzy systems subject to both control input and state constraints. In order to cover a large range of real-world applications, both L2 and L∞ disturbances are considered which result in two different control design procedures. A parameter-dependent version of the generalized sector condition is effectively exploited in a fuzzy Lyapunov control framework to handle the control input saturation. Moreover, the proposed control method is based on the concept of robust invariant set which is able to provide an explicit characterization of the estimated domain of attraction of the closed-loop system. Different optimization algorithms are also proposed to deal with the trade-off between different closed-loop requirements in a local control context. The design conditions are expressed in terms of linear matrix inequalities which can be solved efficiently with available solvers. The numerical examples illustrate how the proposed methodology leads to less conservative results as well as less computational complexity when compared to very recent works in the literature.