Wang, ShiNurdin, HendraZhang, GuofengJames, Matthew2024-05-080005-1098http://hdl.handle.net/1885/317366The purpose of this paper is to present a network realization theory for a class of mixed quantum–classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum–classical systems are proposed. Necessary and sufficient conditions for their physical realizability are derived. Based on these physical realizability conditions, a network synthesis theory for this class of linear mixed quantum–classical systems is developed, which clearly exhibits the quantum component, the classical component, and their interface. An example is used to illustrate the theory presented in this paper.The work was supported by the National Natural Science Foundation of China under Grant No. 61703151, the Natural Science Foundation of Hunan, Province, China (Grant No. 2018JJ3073), Hong Kong RGC Grant (15206915), and the Fundamental Research Funds for the Central Universities (No. 020200-531107050934), AFOSR Grants FA2386-09-1-4089 and FA2386-12-1-4075, the Australian Research Council (DP110102322).application/pdfen-AU© 2018 Elsevier Ltd.Linear stochastic systemsMixed quantum–classical linear stochastic systemsQuantum systemsClassical probabilityQuantum probabilityNetwork synthesis theoryPhysical realizability condition201810.1016/j.automatica.2018.06.0032023-01-08