A complex system approach to root-clustering in separate regions

A novel method which assigns all the poles of a closed-loop system in two specified separate regions of the complex plane is presented. A complex system of degree n, which corresponds to a real system of degree 2n with no real-axis poles, is introduced, and the relation between the feedback-control law of the complex system and that of the real system is derived. In the proposed algorithm, the feedback-control law is determined by using a Riccati equation of the complex system, whose parameters, states, inputs, and outputs are all complex numbers, which corresponds to a real system