Differential algebraic equations (DAEs) consist of a system of differential equations linked to a system of algebraic equations. The differential equations model a dynamic process, while the algebraic equations represent equilibrium relations or equality constraints. DAEs arise naturally in the applied sciences and engineering, for example in electronic circuits, control problems, robotics, and chemical processes. This paper is concerned with the existence of periodic solutions of DAEs of the form Ez’(t)=Az(t)+f(t), where z’=dz/dt, and A and E are constant matrices with detE=0. The input function f is periodic, with period T, and may have jump discontinuities.

The authors rely on the Kronecker-Weierstrass form of linear matrix pencils to analyze the equation. Notice that, because of the periodicity condition, no initial condition is required. Their approach is based on exact solutions, segment concatenation, and periodizer functions. As a result, they obtain exact solutions, thereby avoiding all drawbacks of the Fourier series approach. They complete their study with two practical examples.

The paper is very well written. The objectives are clearly stated in the introduction, with a comparison of existing methods. This work is a very good addition to the literature on periodic solutions of DAEs. It is very well documented, and it will be very useful for mathematicians and engineers working in the area of periodic boundary value problems.