On the detectability and observability of continuous stochastic Markov jump linear systems

This paper is concerned with the detectability and observability of continuous linear stochastic systems subject to Markov jump. By introducing some operators, we investigate the relationship between some different concepts of detectability and observability, and obtain their sufficient and necessary conditions. Continuous-time stochastic Lyapunov equations and stochastic continuous algebraic Riccati equations are also discussed to serve as analysis tools.