Robust Controllability of T–S Fuzzy-Model-Based Control Systems With Parametric Uncertainties

The robust controllability problem for the Takagi–Sugeno (T–S) fuzzy-model-based control systems is studied in this paper. Under the assumption that the nominal T–S fuzzy-model-based control systems are locally controllable (i.e., each fuzzy rule of the nominal T–S fuzzy-model-based control systems has a full row rank for its controllability matrix), a sufficient condition is proposed to preserve the assumed property when the parameter uncertainties are added into the nominal T–S fuzzy-model-based control systems. The proposed sufficient condition can provide the explicit relationship of the bounds on parameter uncertainties to preserve the assumed property. Besides, a robustly global controllability condition and the related robustly global stabilizability condition of the uncertain T–S fuzzy-model-based control systems are also presented in this paper. A nonlinear mass–spring–damper mechanical system with parameter uncertainties is given as an example to illustrate the application of the proposed sufficient conditions.