Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative

Document Type : Research Paper


1 Pakistan Institute of Engineering and Technology, Multan, Pakistan.

2 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.

3 Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Campus, Van, Turkey.


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.