Optimal pole placement in a vertical strip

Abstract

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. And 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.

A new result for closed‐loop poles region of LQ‐optimal discrete‐time systems

“…Anderson and Moore [2] provided a simple design method for a continuous-time LQ optimal system which would result in the prescribed degree of stability by placing the system's eigenvalues to the left of a vertical line at − . Arar et al [3] have presented a method to determine a state-feedback controller which places the closed-loop poles within a vertical strip in the complex plane. Furthermore, Di Ruscio [4] proposed a method to determine the region in which the closed-loop eigenvalues of a continuous-time LQ optimal system are located.…”