Stabilization of networked control systems with multirate sampling

In this paper, we study the stabilization of networked control systems with multirate sampling. The input channels are modeled in two different ways. First, each of them is modeled as the cascade of a downsampling circuit, an ideal transmission system together with an additive norm bounded uncertainty, and a discrete zero-order hold. Then each input channel is modeled as the cascade of a downsampling circuit, an ideal transmission system together with a feedback norm bounded uncertainty, and a discrete zero-order hold. For each channel model, different downsampling rates are allowed in different input channels. The minimum total channel capacity required for stabilization is investigated. The key idea of our approach is the channel resource allocation, i.e., given the total capacity of the communication network, we do have the freedom to allocate the capacities among different input channels. With this new idea, we successfully show that the multirate networked control system with each channel model can be stabilized by state feedback under an appropriate resource allocation, if and only if the total network capacity is greater than the topological entropy of the plant. We also apply the result to multirate quantized control systems. Both the commonly used logarithmic quantizer and the alternative logarithmic quantizer are considered. For each case, a sufficient condition for stabilization is obtained which involves a trade-off between the densities of time quantization and spatial quantization.