Abstract Linear time-invariant systems of the form are considered. The problem is to find a control vector u(t) that will drive the state of this system from a given z(0) to some (not necessarily fixed) final state z(t f ) in some (not necessarily fixed) time t f while minimizing a cost functional of the form The original system is re-written in the form of a descriptor-variable system consisting of the equations diag It is shown that there is a matrix such that thus the original optimal control problem is equivalent to the following problem. Find a control vector u(t) that drives the descriptor vector x(t) from a given x(0) to some x(t f ) while minimizing Using the results of an earlier paper on optimal control of descriptor systems (Ibrahim et al. 1988), necessary conditions are derived for the existence of minima of ; the problem of finding sufficient conditions for the existence of minima of is not considered. Various formulae are obtained for designing open-loop controls corresponding to three diffe...