On the solvability of singular linear system with Markov jump parameters

This paper extends the solvability property of standard singular systems to singular systems with Markov jump parameters. In the literature, the procedure for checking solvability for this class of systems involves a certain collection of matrices and does not fully reflect the stochastic features of the system. We present two new notions of solvability that take into account the stochastic nature of the system and provide information about the behavior of the first and second conditional moments. Numerical examples illustrate the differences among the proposed notions of solvability and the existing one.