Robust stabilization of model-based uncertain singularly perturbed systems with networked time-delay

In this paper, a robust stabilization of the uncertain singularly perturbed system via a networked state feedback with the transmission time-delay is addressed. Taking its nominal system as a model plant, propagation unit and overall states chosen to overcome the difficulty of communication delay, the characterization of singular perturbation for the overall hybrid system is still preserved on each sampling interval. Since the traditional two-time-scale technique is not applicable for the overall hybrid system, its approximated slow and fast subsystems are constructed. Based on the decomposition, the approximated slow and fast test matrix for the stability is established. Then, Tikhonov-like limit process of the stability test matrix for the overall hybrid system is proved. It is shown by this Tikhonov-like result that there exists a bound of the small parameter to guarantee global exponential stability of the overall hybrid system on the time interval if the eigenvalues of a lower order slow test matrix are strictly inside its unit circles. Further, a structure analysis of the approximated slow test matrix is developed. Finally, a numerical simulation is presented to illustrate the main results.