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∞H∞ performance index is defined, which extends the standard H∞H∞ performance. Then, a sufficient condition is derived such that the fuzzy closed-loop system satisfies a finite-frequency H∞H∞ 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.