Geodesic
Feedback and Impulse Behavior of Differential-Algebraic Equations
Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 610-629

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A controlled linear system of differential-algebraic equations with infinitely differentiable coefficients is considered. An arbitrarily high unsolvability index and a variable rank of matrix coefficients are allowed. Sufficient existence conditions are obtained and methods are proposed for finding a feedback control such that the solution of a closed system exists in the class of generalized function (distribution)s of Sobolev–Schwartz type and does not contain singular terms. This control is constructed as a linear combination of the components of the system's state and its derivatives.
Keywords: differential-algebraic equations, generalized solution, feedback, exclusion of impulse terms. 
@article{MZM_2021_110_4_a11,
     author = {A. A. Shcheglova},
     title = {Feedback and {Impulse} {Behavior} of {Differential-Algebraic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {610--629},
     publisher = {mathdoc},
     volume = {110},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a11/}
}
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A. A. Shcheglova. Feedback and Impulse Behavior of Differential-Algebraic Equations. Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 610-629. http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a11/