  In this paper, a method is proposed to solve the problem of monotone
smoothing splines using general linear systems. This problem, also called
monotone control theoretic splines, has been solved only when the curve
generator is modeled by the second-order integrator, but not for other cases.
The difficulty in the problem is that the monotonicity constraint should be
satisfied over an interval which has the cardinality of the continuum. To solve
this problem, we first formulate the problem as a semi-infinite quadratic
programming, and then we adopt a discretization technique to obtain a
finite-dimensional quadratic programming problem. It is shown that the solution
of the finite-dimensional problem always satisfies the infinite-dimensional
monotonicity constraint. It is also proved that the approximated solution
converges to the exact solution as the discretization grid-size tends to zero.
An example is presented to show the effectiveness of the proposed method.
