Reduced-order model approximation of fuzzy switched systems with pre-specified performance

The reduced-order model approximation problem for discrete-time hybrid switched nonlinear systems is addressed via Takagi-Sugeno (T-S) fuzzy modelling in this paper. For a high-dimension hybrid switched nonlinear system, our aim is on how to construct a reduced-dimension hybrid switched model, approximating its original high-order model well with a pre-specified system performance level. Firstly, the mean-square exponential stability analysis is provided, in which it guarantees the given weighted H∞ system performance level for the augmented error dynamic system by the average dwell time analysis approach and the hybrid switched Lyapunov stability theory. The solution of corresponding model reduction problem with pre-specified performance is given by using the projection Lemma. The algorithm of the reduced-order hybrid switched model parameters is designed by the cone complementary linearization technique. Finally, the advantage and effectiveness of the proposed reduced-order model approximation approach are shown by the simulation result.