On the observability and detectability of continuous-time Markov jump linear systems

The paper introduces a new detectability concept for continuous-time Markov jump linear systems with finite Markov space that generalizes previous concepts found in the literature. The detectability in the weak sense is characterized as mean square detectability of a certain related stochastic system, making both detectability senses directly comparable. The concept can also ensure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is unique and stabilizing, making other concepts redundant. The paper also obtains a set of matrices that plays the role of the observability matrix for deterministic linear systems, and it allows geometric and qualitative properties. Tests for weak observability and detectability of a system are provided, the first consisting of a simple rank test, similar to the usual observability test for deterministic linear systems. The complete results are presented in [E.F. Costa et al., 2002].