Non-monotonic Lyapunov function based membership function dependent robust control of Takagi–Sugeno fuzzy systems

In the tasks of output robust stabilization control for discrete-time Takagi–Sugeno (T–S) fuzzy systems, a novel method is proposed to give better control performance and relax the conservatism. Firstly, a robust control method based on membership functions dependent (MFD) is obtained by utilizing a classic piecewise linear function approximation approach. A traditional membership functions independent (MFI) robust synthesis method is also presented. Subsequently, a new non-monotonic $H_{\infty }$ robust control concept is proposed to better describe the system performance more comprehensively. Then, based on the non-monotonic Lyapunov function (NLF) approaches, system non-monotonic robust conditions are established in the form of linear matrix inequalities (LMl) with reduced conservatism. Finally, two simulation examples are utilized to verify the validity of the designed methods.