Observer‐based non‐PDC controller design for T–S fuzzy systems with the fractional‐order

Abstract

This study focuses on observer‐based non‐parallel‐distributed‐compensation (non‐PDC) controller design for T–S fuzzy systems with fractional‐order . A rule‐dependent fuzzy Lyapunov function is used to analyse the (non‐PDC) controller. For a dynamical output feedback design, the immeasurable premise variables of the fuzzy observer and fuzzy controller are considered. Under the assumption that the membership derivatives for a given compact set can be represented by a kind of weighted sum, the difficulty in knowing a priori the appropriate bounds of the membership derivatives to satisfy linear matrix inequalities (LMIs) is removed. Using the matrix singular value decomposition method, new less‐conservative strict LMI conditions are derived for the locally asymptotical stabilisation of the fractional‐order T–S fuzzy system with immeasurable state variables. A fractional‐order Lorenz chaotic system is provided to show the effectiveness of the proposed method.