Quantized sampled-data feedback stabilization for linear and nonlinear control systems

We propose a new control strategy which uses quantized sampled data of the states (i.e., incomplete knowledge of the states) with quantizer sensitivities that vary (i.e., depend on the values of the states) as the system evolves. The resulting closed-loop system may be viewed as a hybrid system that incorporates discrete event driven data that act upon the continuous-time component (the plant) of the entire system. For linear systems that are stabilizable by linear time-invariant feedback, we propose a quantized sampled-data control policy which globally and exponentially stabilizes the systems. Furthermore, we show that by appropriately choosing the saturation levels, the proposed control policy is robust in the presence of certain classes of perturbations. We also study the local stabilization and robustness problems for nonlinear control systems via linearization.