H∞ controller design for affine fuzzy systems based on piecewise Lyapunov functions in finite-frequency domain

This paper studies the problem of state feedback controller design for a class of nonlinear systems described by continuous-time affine fuzzy models. Based on a piecewise continuous Lyapunov function combined with S-procedure and some matrix decoupling techniques, a novel control law is derived in the formulation of linear matrix inequalities (LMIs) in finite-frequency domain. First, a so-called finite-frequency H-infinity performance index is defined, which extends the standard H-infinity performance. Then, a sufficient condition is derived such that the fuzzy closed-loop system satisfies a finite-frequency H-infinity performance. By introducing the S-procedure and adding slack variables, piecewise controllers are designed to deal with disturbances in the low-, middle-, and high-frequency domain, respectively. The proposed piecewise controller design method can get a better disturbance-attenuation performance when the frequency ranges of disturbances are known beforehand. Finally, two examples are given to illustrate the effectiveness and superiority of the new results. (C) 2015 Elsevier B.V. All rights reserved.