Zehra, Anum; Younus, Awais; Tunc, Cemil Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative. (English) Zbl 1513.34237 Comput. Methods Differ. Equ. 10, No. 1, 200-214 (2022). 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 Keywords:controllability; observability; Drazin inverse; Caputo fractional derivative PDFBibTeX XMLCite \textit{A. Zehra} et al., Comput. Methods Differ. Equ. 10, No. 1, 200--214 (2022; Zbl 1513.34237) Full Text: DOI References: [1] I. Tejado, D. Valerio, and N. Valerio,Fractional calculus in economic growth modelling: the Spanish and Portuguese cases., Int. J. Dyn. Control,5(1) (2017), 208-222. [2] L. A. Vlasenko and N. A. Perestyuk,On the solvability of differential-algebraic equations with impulse action, (Russian) Ukran. Mat. Zh.,57(4) (2005), 458-468; translation in Ukrainian Math. 57(4) (2005), 551-564 · Zbl 1102.34004 [3] W. Wulling,The Drazin inverse of a singular, unreduced tridiagonal matrix, Linear Algebra and its Applications, 439(10) (2013), 2736-2745. · Zbl 1283.15020 [4] A. Younas, I. Javaid, and A. Zehra,On controllability and observability of fractional continuous time linear systems with regular pencils, Bulletin of the Polish Academy of Sciences Technical Sciences,65(3) (2017), 297-304. [5] X.F. Zhou, S. Liu, and W. Jiang,Complete controllability of impulsive fractional linear time invarient systems with delay, Abst. Appl. Anal., (2013), ID 374938 · Zbl 1291.34129 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.