Hybrid stabilization of linear time-invariant systems with two quantizers

We consider stabilizing a discrete-time linear time-invariant system via state feedback where both quantized state and input signals are involved. The system in consideration is stabilizable and a stabilizing state feedback is designed without considering quantization, but the system's stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of the quantizer parameters are updated at discrete instants of time.