1. Stochastic stability in Max-Product and Max-Plus Systems with Markovian Jumps
- Author
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George P. Papavassilopoulos, Petros Maragos, Ioannis Kordonis, School of of Electrical and Computer Engineering [Athens] (School of E.C.E), National Technical University of Athens [Athens] (NTUA), and Dept. of Electrical and Computer Engineering
- Subjects
Lyapunov function ,0209 industrial biotechnology ,Stochastic stability ,Markov process ,Systems and Control (eess.SY) ,02 engineering and technology ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,020901 industrial engineering & automation ,Stability theory ,FOS: Electrical engineering, electronic engineering, information engineering ,FOS: Mathematics ,Nonlinear systems ,[INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY] ,Applied mathematics ,0101 mathematics ,Electrical and Electronic Engineering ,Mathematics - Optimization and Control ,Mathematics ,Max-plus systems ,Stochastic systems ,State (functional analysis) ,Optimization and Control (math.OC) ,Control and Systems Engineering ,Product (mathematics) ,symbols ,Computer Science - Systems and Control ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Isomorphism ,Focus (optics) - Abstract
International audience; 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.
- Published
- 2018
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