Stabilization of discrete-time linear systems with quantization and arbitrary packet losses

In this paper, we mainly focus on the stabilization problem of discrete-time linear systems with both quantized input feedback and arbitrary packet losses. The coarsest quantization strategy is analyzed in detail to guarantee the asymptotic stability of the system. If the coarsest quantizer is logarithmic, the necessary and sufficient conditions to asymptotically stabilize such system are converted into some algebraic Riccati equations and then into some LMIs. Then the infimum of the quantization density for the logarithmic quantizer over all packet loss dependent Lyapunov functions is obtained according to these LMIs. In addition, we also prove that the sector bound approach for the logarithmic quantizer is still valid for the system with arbitrary packet losses. The problem of asymptotic stability can be converted into a robust control problem with sector bound uncertainties. The robust stability of the uncertain system is formulated into some LMIs. Finally, an example is given to show the effectiveness of the results obtained in this paper.