Mode-dependent non-fragile observer-based controller design for fractional-order T–S fuzzy systems with Markovian jump via non-PDC scheme

Abstract

Abstract In this paper, controller synthesis problem based on non-fragile observer is investigated for a class of fractional-order nonlinear systems subject to abrupt changes under the fractional-order T–S fuzzy model with Markovian jump. By utilizing non-parallel-distributed-compensation (non-PDC) scheme, the model-dependent observer and the observer-based fuzzy controller are designed under imperfect premise matching to enhance design flexibility. Moreover, the multiplicative random sensor noise over the measurement output is considered. Then, based on the matrix singular value decomposition method (SVD) and the membership-function-shape-dependent (MFSD) analysis approach, new less-conservative sufficient conditions in term of LMIs are derived to guarantee the closed-loop fractional-order fuzzy system robustly stochastically stable. Finally, two examples are provided to illustrate the effectiveness of the new design techniques for fractional-order systems.