A mixed deterministic and stochastic small gain theorem and its application to networked stabilization

When both quantization and multiplicative noise are considered in a networked control system (NCS), the closed-loop involves both deterministic and stochastic uncertainties. Classical small gain theorems can handle the system stability with only one type of the uncertainties and hence need to be extended. In this paper we propose such a small gain theorem. The stochastic uncertainty is integrated with the linear time-invariant plant, and the stability condition of such systems with respect to deterministic uncertainties is characterized. Finally we apply the result to the NCS problem and acquire the stabilizability condition for the NCS.