Transmission probability condition for stabilisability of networked control systems

Abstract

In this study, the authors study the stabilisability of networked control systems (NCSs) with random packet dropout, where the network packet loss is modelled as an i.i.d. Bernoulli process. Two commonly used strategies compensating for the lost signal, namely, ‘zero signal’ and the ‘last available signal’ strategy are compared. First, NCSs with the ‘zero signal’ strategy is considered. Several necessary and sufficient conditions for stabilisability are established and further analysis of it is conducted. A critical transmission probability (CTP) is introduced, which is the least required transmission probability for the purpose of stabilising a networked plant. An explicit formula for CTP is derived and it shows that the CTP is merely dependent on the unstable poles of the plant. The authors theoretically validate that the least required information for stabilising a plant has an explicit relationship with the degree of instability of its own. Then a necessary condition for the stabilisability of NCSs with the ‘last available signal’ strategy is proposed. It is theoretically proved that the ‘last available signal’ strategy cannot compensate the effect of loss data better than the ‘zero signal’ does. Two illustrative examples are provided to show the validity of the proposed results.