The mean-square stabilization of networked feedback systems with channel delays

This work studies a stabilization problem via output feedback for networked linear time-invariant (LTI) discrete-time systems with quantization effects and network-induced delays. Logarithm quantization laws are adopted in the systems and the quantization errors are modeled as multiplicative noises. The network-induced delays under consideration are fixed delays. The necessary and sufficient condition of mean-square stabilization is studied for a SISO LTI networked control system. And then an analytic expression for the trade-off between quantization noise and channel delays in the mean-square stabilization problem is presented. The largest quantization noise variance with which the mean-square stability of the networked feedback system is guaranteed is obtained in terms of the fixed channel delay. While, the largest delay step which is allowed in the systems is obtained for a given quantization noise variance. Moreover, these results are extended to the case for minimum phase MIMO LTI systems.