Robustness design of fuzzy controllers for nonlinear multiple time-delay singularly perturbed systems: using dither as auxiliary

The stabilisation problem is considered in this study for nonlinear multiple time-delay singularly perturbed (NDSP) systems. First, a neural-network (NN) model is employed to approximate the reduced-order model of the NDSP plant. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, a robustness design of fuzzy control is proposed to stabilise the NDSP system. If the designed fuzzy controller cannot stabilise the NDSP system, a dither (as an auxiliary of the fuzzy controller) is simultaneously introduced to stabilise the NDSP system. If the frequency of dither is high enough, the outputs of the dithered system and its corresponding mathematical model, the relaxed system, can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered system by establishing that of the relaxed system. Finally, this study provides a numerical example with simulations to illustrate the concepts discussed throughout this article.