Stochastic stability of positive Markov jump linear systems. (English) Zbl 1298.93336
Summary: This paper investigates on the stability properties of Positive Markov Jump Linear Systems (PMJLS’s), i.e. Markov Jump Linear Systems with nonnegative state variables. Specific features of these systems are highlighted. In particular, a new notion of stability (Exponential Mean stability) is introduced and is shown to be equivalent to the standard notion of 1-moment stability. Moreover, various sufficient conditions for Exponential Almost-Sure stability are worked out, with different levels of conservatism. The implications among the different stability notions are discussed. It is remarkable that, thanks to the positivity assumption, some conditions can be checked by solving linear programming feasibility problems.
MSC:
| 93E12 | Identification in stochastic control theory |
| 60J75 | Jump processes (MSC2010) |
| 93C05 | Linear systems in control theory |
| 90C05 | Linear programming |
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