Coarsest quantization for networked control of uncertain linear systems

In the design of networked control systems, one must take account of communication constraints in the form of data rate. In this paper, we consider a quantized control problem for stabilizing uncertain linear systems in the sense of quadratic stability. For a class of finite-order (possibly time-varying) uncertain autoregressive plants, we show that the coarsest quantizer for achieving quadratic stabilization is of logarithmic type. In particular, for a given quadratic Lyapunov function, the largest coarseness is derived in an analytic form. The result explicitly shows that plants with more uncertainties require more precise information in the quantized signals to achieve quadratic stabilization. We also provide a numerical method based on a linear matrix inequality to search for a Lyapunov function along with a quantizer of a given level of coarseness.