Optimal pole placement in a vertical strip

A recursive method for determining the state weighting matrix of a linear quadratic regulator problem in order to shift the open loop poles inside a vertical strip is presented. This method is capable of shifting the real and imaginary parts for continuous time systems. Aggregation is used in each step of the recursive process. Therefore each time the order of the system is reduced to first or second order. A constrained minimization problem with linear and nonlinear constraints has to be solved in order to find the state weighting matrix of the reduced order system that will shift the open loop poles inside the vertical strip