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Article Dans Une Revue Automatica Année : 2018

Stochastic stability in Max-Product and Max-Plus Systems with Markovian Jumps

Résumé

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.

Dates et versions

hal-02073986 , version 1 (20-03-2019)

Identifiants

Citer

Ioannis Kordonis, Petros Maragos, George P. Papavassilopoulos. Stochastic stability in Max-Product and Max-Plus Systems with Markovian Jumps. Automatica, 2018, 92, pp.123-132. ⟨10.1016/j.automatica.2018.03.008⟩. ⟨hal-02073986⟩
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