Approximate models of stochastic linear quantized control systems

This paper considers a feedback control system where a plant is actuated by a quantized control. The measurements are assumed to be disturbed by an additive wideband noise in the feedback loop. The nonlinear control in the presence of the noise may cause the system to be variable structure. Variable structure systems (VSS) disturbed by noise exhibit sliding modes on the switching manifold. If the quantizer causes a high gain in the system due to quantization of a small measurement for a fixed quantization level, the quantized control systems can be represented by a singularly perturbed model and analyzed by two approximate reduced-order models. It is shown that the slow model approximates the system in the sliding mode with an error of an order of the estimated singular perturbation parameter.