Optimal control of processes whose descriptions involve pure imaginary singularities

Concerns the development of Laplace transform domain methods of finding quadratic optimal controls for multivariable linear dynamical systems acted on by stochastic disturbances. The methods presume that the plant to be controlled is described by multivariable transfer functions. The optimal control problem is outlined, and Austin´s method (1979) is presented and extended to the case of plants having such pure imaginary poles. It is shown that the solution procedures already established for plants presumed not to have such poles may actually be used for plants incorporating such poles. This is proved by investigating these procedures for deriving optimal controls and proving that poles on the imaginary axis do not appear in expressions where they would cause mathematical difficulty with an integrator is presented