Abstract
Linear constant coefficient optimum control problems with a quadratic cost functional which is not limited to be positive semi-definite are treated in this paper. If the quadratic cost functional is not positive semi-definite, then the problem often becomes a trivial one so that the problem can not be solved or the cost diverges to -∞. This paper shows the condition of the weighting matrices of the cost functional under which the problem has a nontrivial solution so that the constructed system is a stable one with constant coefficients, achieving the exact minimum of the cost functional.
