On the stability in probability of Markov jump systems with quadratic terms

The note presents conditions to assure the stability in probability for a class of continuoustime quadratic Markov jump systems. From the viewpoint of the state-space evolution, the system has two parts: (i) a linear term, in which the matrix parameter jumps according to a Markov chain, and (ii) a quadratic term with no jumps. The stability in probability for the quadratic Markov jump system is then assured under mild conditions. A numerical example illustrates the usefulness of the derived results.The note presents conditions to assure the stability in probability for a class of continuoustime quadratic Markov jump systems. From the viewpoint of the state-space evolution, the system has two parts: (i) a linear term, in which the matrix parameter jumps according to a Markov chain, and (ii) a quadratic term with no jumps. The stability in probability for the quadratic Markov jump system is then assured under mild conditions. A numerical example illustrates the usefulness of the derived results.Peer Reviewe