On order reduction and stability analysis of singularly perturbed T-S fuzzy models

This note considers the stability problem of the discrete Tagagi-Sugeno (T-S) fuzzy models described locally by nonlinear models with two-time-scale property. An explicit form transforming the two-time-scale process into a standard singularly perturbed form is provided and, slow and fast decoupled fuzzy subsystems are synthesized. A design procedure is formulated by which the stability of initial T-S fuzzy system can be formed through the stability of the slow and fast fuzzy subsystems. Vector norms and characteristic state matrices in the arrow form are adopted to examine the stability of introduced systems. This theoretical analysis is illustrated by a numerical example.