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

Abstract

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 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