Periodic solutions of semi-explicit differential-algebraic equations with time-dependent constraints

In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized differential-algebraic equations with non-autonomous constraints of a particular type. We provide simple, degree-theoretic conditions for the existence of branches of T-periodic solutions of the considered equations. Our approach is based on topological arguments as regards differential equations on implicitly defined manifolds, combined with elementary facts of matrix analysis.