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Supervision of Flexible Manufacturing Systems
A Proof of Proposition 2 1 1
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behavior boundary points buffer buﬁer buﬂer CAF policy Chapter closed switched server compute contain continuous variables converges convex coset deﬁne deﬁnition dimensional discrete events discrete time system equation equivalence relation ergodic ergodic theory Euclidean topology example exists extremal point ﬁnd ﬁnite number Finite Observability Congruence ﬁrst ﬁxed ﬂexible manufacturing system idling condition implies indicator function inﬁnitely initial condition interior Lemma limit cycle limit point linear Markov maps lower bound machine map g Markov chain measure mode multi-modal system n-complete nonempty Note parameters piecewise linear piecewise linear Markov production runs Proof result satisﬁed Scheduled Controller scheduling policy Section setup Speciﬁcally stable Statistical Stability subset subsystem Supervision of Flexible switched arrival system switched server system switching function policy switching points switching region policy switching sequence switching set Theorem trajectory unit interval vector ﬁeld zero