Linear time-invariant systems of the form are considered, and the problem is as follows. Find a control vector u[t) that will drive the state vector z(t) from a fixed z(0) to a prescribed z(tr) in some fixed final time t, while minimizing a cost functional of the form First, the state-variable system is re-written in the descriptor-variable form diag{Ip} is P+. Then, using a variational method developed previously, a formula is obtained that yields a set of input vectors making the first variation of J zero. Substitution of this input formula into J leads to a scalar-valued functional of several scalar variables that is minimized by the standard Lagrange-multiplier method. The results of the paper may also be used to find inputs that satisfy some prescribed boundary conditions while minimizing