On stability and detectability of complex stochastic systems

Stability and detectability of stochastic systems are essential and important concepts in control theory which have been a popular research direction in recent years. However, most study about stability and detectability are concentrated on real stochastic systems instead of complex stochastic systems. In this paper, the matrix transformation approach is used to study asymptomatical mean square stability, critical stability, D-stability and detectability of continuous-time complex stochastic systems. With the aid of the spectral analysis technique, we can obtain some practical criteria for stability and detectabilit. Moreover, some useful properties of the generalized Lyapunov equation are derived based on critical stability and exact detectability of complex stochastic systems.