Degree of disturbance rejection capability for linear anti-stable systems

Controllability is a structural property that carries information useful for control system design. There are several measures to determine the location of actuator, and one of them is degree of disturbance rejection capability (DODR). DODR is a quantitative measure representing how controllable the system is under the presence of persistent disturbance. However, this measure is defined in asymptotically stable systems, not in unstable systems. Thus, the problem to apply the measure to unstable system still remains. In this paper, therefore, the way to apply DODR to anti-stable systems is proposed as preliminary research. The definition of the measure is same with existing measure of DODR. We used Gramians of a system which has poles in the mirror image side of the original given system.