We present an extension of recent semidefinite programming formulations for atomic decomposition over continuous dictionaries, with applications to continuous or 'gridless' compressed sensing. The dictionary considered in this paper is defined in terms of a general matrix pencil and is parameterized by a complex variable that varies over a segment of a line or circle in the complex plane. The main result of the paper is the formulation as a convex semidefinite optimization problem, and a simple constructive proof of the equivalence. The techniques are illustrated with a direction of arrival estimation problem, and an example of low-rank structured matrix decomposition.