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Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative. (English) Zbl 1513.34237

Summary: Linear impulsive fractional differential-algebraic systems (LIFDAS) in a finite dimensional space are studied. We obtain the solution of LIFDAS. Using Gramian matrices, necessary and sufficient conditions for controllability and observability of time varying LIFDAS are established. We acquired the criterion for time-invariant LIFDAS in the form of rank conditions. The results are more generalized than the results that are obtained for various differential-algebraic systems without impulses.

MSC:

34H05 Control problems involving ordinary differential equations
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
34A37 Ordinary differential equations with impulses
93B05 Controllability
93B07 Observability
34A30 Linear ordinary differential equations and systems
34A09 Implicit ordinary differential equations, differential-algebraic equations
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References:

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