H∞ output feedback control for fractional-order T-S fuzzy model with time-delay

This paper addresses H∞ observer-based control issue for fractional-order uncertain Takagi-Sugeno (T-S) fuzzy model with unknown input and time-delay in the case of system order in (0,1). In order to construct the state estimation variables, reduced-order fuzzy observer is devised. By utilizing Lyapunov method of fractional-order derivative, the sufficient conditions are provided to ensure the effectiveness of proposed reduced-order unknown input observer and the stabilization of augmented T-S fuzzy model with an H∞-norm σ. The conditions are shown in terms of linear matrix inequalities (LMIs) and the matrices of unknown input fuzzy observer are computed by relevant LMIs. Furthermore, by solving LMIs, the T-S fuzzy output feedback control is realized. Finally, a numerical example and a single-link robot arm example are simulated to illustrate the validity of the addressed strategy.