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Fractional positive continuous-time linear systems and their reachability. (English) Zbl 1235.34019

Summary: A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.

MSC:

34A08 Fractional ordinary differential equations
34A30 Linear ordinary differential equations and systems
34H05 Control problems involving ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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