Robust quantised control of hybrid stochastic systems based on discrete-time state and mode observations

In this paper, the problems of robust quantized feedback control are studied for hybrid stochastic systems based on discrete-time observations of state and mode. All of the existing results in this area design the quantized feedback control based on continuous observations of the state and mode for all time t ≥ 0 (see [23–25]). This is the first paper where we propose to use the quantized feedback control based on discrete-time observations of the state and mode. The key reason for this is to reduce the burden of communication by using not only the quantization (i.e. in the direction of state axis), but also discrete-time observations of state and mode (i.e. in the direction of time axis). Thus, the designed quantized feedback controllers have to be based on the discrete-time observations of state and mode. Clearly, the new quantized feedback controllers are more realistic and cost less in practice. Two examples with computer simulations will be provided to illustrate the effectiveness of the proposed control method.