Algebraic invariance conditions in the study of approximate (null-)controllability of Markov switch processes
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We aim at studying approximate null-controllability properties of a particular class of piecewise linear Markov processes (Markovian switch systems). The criteria are given in terms of algebraic invariance and are easily computable. We propose several necessary conditions and a sufficient one. The hierarchy between these conditions is studied via suitable counterexamples. Equivalence criteria are given in abstract form for general dynamics and algebraic form for systems with constant coefficients or continuous switching. The problem is motivated by the study of lysis phenomena in biological organisms and price prediction on spike-driven commodities.
KeywordsApproximate (null-)controllability Controlled piecewise deterministic Markov process Markov switch process Invariance Stochastic gene networks
The work of the first author has been partially supported by he French National Research Agency Project PIECE, number ANR-12-JS01-0006.
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