# Stability Analysis of Positive Semi-Markovian Jump Linear Systems with State Resets

@article{Ogura2014StabilityAO, title={Stability Analysis of Positive Semi-Markovian Jump Linear Systems with State Resets}, author={Masaki Ogura and Clyde F. Martin}, journal={SIAM J. Control. Optim.}, year={2014}, volume={52}, pages={1809-1831} }

This paper studies the mean stability of positive semi-Markovian jump linear systems. We show that their mean stability is characterized by the spectral radius of a matrix that is easy to compute. In deriving the condition we use a certain discretization of a semi-Markovian jump linear system that preserves stability. Also we show a characterization for the exponential mean stability of continuous-time positive Markovian jump linear systems. Numerical examples are given to illustrate the…

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## 39 Citations

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The stability optimization problem reduces to a convex optimization problem under certain regularity conditions on the system matrices and the cost function by using a result from the matrix theory on the log-log convexity of the spectral radius of nonnegative matrices.

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