Filter Design for Positive T–S Fuzzy Continuous-Time Systems With Time Delay Using Piecewise-Linear Membership Functions

This article focuses on the filtering problem and stability analysis for positive Takagi-Sugeno (T-S) fuzzy systems with time delay under L 1 -induced performance. Due to importance of estimation system states but few filter design results nonlinear systems, it is an attractive meaningful topic well worth studying. In order fully exploit take advantage positivity T-S many commonly used methods, instance free-weighting matrix approach similarity transformation are probably not suitable systems. To address hard-nut-to-crack problem, auxiliary variable introduced so that augmentation can be employed carry out error addition, another obstacle cannot ignored existence nonconvex terms in conditions. For getting around this barrier, some iterative linear inequality algorithms have been proposed literature. However, considering weakness these methods guarantee convergence a numerical solution process exhaustive, we present effective decoupling method convert conditions into convex ones article. Furthermore, copositive Lyapunov function, which incorporates at same chosen characteristic captured further. because plenty valuable information membership functions being ignored, hence, obtained conservative. sake relaxing conservativeness, advanced piecewise-linear approximate utilized facilitate analysis. Therefore, relaxed conditions, cast as sum squares (SOS) solved numerically. Finally, effectiveness designed strategy satisfying performance demonstrated by simulation example.