About symmetrical transformation of the spectrum of the unstable object when controlling with criterion of the minimum of the energy expenses
AbstractThis article is considering stationary linear object, which have strictly positive real parts of all characteristic values (the spectrum). It is shown, that if the control is providing minimum of the integral of the square of control signal, spectrum of the object is symmetrically displaying in the left half of the complex plane. Proof and example are presented.
Keywords:spectrum of a matrix , the unstable object, optimum control, dynamic programming, linear law with limit of control , the attraction area , the symmetrical transformation.