The purpose of this paper is to discuss, by the use of the Balakrishnan’s epsilon method, a class of optimal control problems governed by continuous linear time invariant singular systems which have only a finite dynamic mode. The linear differential algebraic equation is handled using the epsilon technique to obtain a sequence of the calculus of variations problems. A convergence theorem is given to obtain approximate and, in the limit, an optimal solution of this class of optimal control problem by the use of the necessary optimality conditions of Euler–Lagrange type. A correspondence has been also shown between this penalty function and duality for this class of optimal control problems considered. As an application, an example of optimal linear quadratic problem is also given.

We investigate different concepts related to the controllability of linear constant coefficient differentialalgebraic equations. Concepts like impulse controllability, controllability at infinity, strong and complete controllability are described and defined by using an equivalent form for linear time-invariant singular systems. Some real-life problems are given to illustrate the presented theory.