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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...
In this paper, stochastic stability for discrete-time singular systems with Markov jump parameters is addressed. We present a set of coupled generalised Lyapunov equations (CGLEs) that serves as a necessary and sufficient condition for stochastic stability. A method for solving the obtained CGLEs is also presented, based on iterations of usual descriptor Lyapunov equations. An illustrative example...
The paper introduces weak controllability and weak stabilizability concepts for discrete-time Markov jump linear system with finite Markov space. We introduce a collection of matrices Copf that resembles controllability matrices of deterministic linear systems. The collection of matrices Copf allows us to define a weak controllability concept by requiring that the matrices are full rank, as well as...
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