The stabilizability and detectability of continuous-time complex stochastic systems

In control theory, the stabilizability and detectability of stochastic systems are very basic and important concepts and have been extensively studied. Previous studies mainly focused on the real system instead of complex stochastic system. In this paper, matrix transformation approach is used to convert complex stochastic system to the corresponding real systems. Firstly, with the use of spectrum analysis method, the stabilizability of corresponding real stochastic systems are studied and then we can obtain some practical criteria for the stabilizability and detectability of continuous-time complex stochastic systems. Secondly, with the same approach the definitions of detectability of continuous-time complex stochastic systems including stochastic detectability, exact detectability and complete detectability are studied and numerical examples are derived.