Necessary and sufficient conditions to the transitivity in simultaneous stabilisation of time-varying systems

In this study, the authors study the transmission problem in simultaneous stabilisation of discrete time-varying systems in the frame work of nest algebra. The necessary and sufficient conditions are developed for the transitivity and strong transitivity in simultaneous stabilisation, respectively. Some criterions for these two properties are established in terms of singly strong representations of only one or two given plants but not all. Finally, the authors give parameterisations of simultaneous stabilisers when the properties of transitivity hold.