2018 |
Ioannis Kordonis, Petros Maragos, George P Papavassilopoulos Stochastic stability in Max-Product and Max-Plus Systems with Markovian Jumps Journal Article Automatica, 92 , pp. 123–132, 2018, ISSN: 00051098. Abstract | BibTeX | Links: [PDF] @article{348, title = {Stochastic stability in Max-Product and Max-Plus Systems with Markovian Jumps}, author = {Ioannis Kordonis and Petros Maragos and George P Papavassilopoulos}, url = {http://robotics.ntua.gr/wp-content/uploads/publications/KMP_StochStabilityInMPsystemsMarkovJumps_Automatica_preprint.pdf}, doi = {10.1016/j.automatica.2018.03.008}, issn = {00051098}, year = {2018}, date = {2018-01-01}, journal = {Automatica}, volume = {92}, pages = {123--132}, abstract = {We study Max-Product and Max-Plus Systems with Markovian Jumps and focus on stochastic stability problems. At first, a Lyapunov function is derived for the asymptotically stable deterministic Max-Product Systems. This Lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of Max-Product systems with Markovian Jumps. Many step Lyapunov functions are then used to derive necessary and sufficient conditions for stochastic stability. The results for the Max-Product systems are then applied to Max-Plus systems with Markovian Jumps, using an isomorphism and almost sure bounds for the asymptotic behavior of the state are obtained. A numerical example illustrating the application of the stability results on a production system is also given.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study Max-Product and Max-Plus Systems with Markovian Jumps and focus on stochastic stability problems. At first, a Lyapunov function is derived for the asymptotically stable deterministic Max-Product Systems. This Lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of Max-Product systems with Markovian Jumps. Many step Lyapunov functions are then used to derive necessary and sufficient conditions for stochastic stability. The results for the Max-Product systems are then applied to Max-Plus systems with Markovian Jumps, using an isomorphism and almost sure bounds for the asymptotic behavior of the state are obtained. A numerical example illustrating the application of the stability results on a production system is also given. |
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