Singular Perturbation Analysis for Linear Systems with Vector Quantized Control

In this paper, the analysis for a singularly perturbed linear system with quantization in the feedback loop is performed. It is found that the system has variable structure and can exhibit sliding behavior on the switching surfaces. Because the system is nonsmooth and standard singular perturbation techniques are not applicable, a new technique is developed for a two-input case to obtain the boundary layer solution and the outer solution. A discussion of the approximation error is included. The technique developed is successfully illustrated on a numerical example.