The parameterization of all extended semi-strongly stabilizing controllers with a pole at the origin and two pairs of poles on the imaginary axis

A strongly stabilization is the control method to make control systems stable using stable controllers. Using this method, it is possible to construct a highly reliable control system because it has robustness. The controller needs a pole at the origin to follow the step reference input without steady-state error. A semi-strongly stabilizing controller is proposed that has a pole at the origin and the others in the open left half plane. In some cases, the controller needs to have poles on the imaginary axis; for example, the control systems follow sinusoidal signals and the self-repairing control systems with faulty sensors using resonance. Therefore, Kimura proposed extended semi-strongly stabilizing controllers with poles on the imaginary axis and other poles in the open left-half plane. Niiyama propose control system with failure detection by adapting the extended semi-strongly stabilizing controller to the self-repairing control system with failure sensor using resonance. However, this method remains an error between the output and the reference input. To eliminate this error the controller needs a pole at the origin and two pairs of poles on the imaginary axis. In this paper, to overcome this problem, we propose an extended semi-strongly stabilizing controller with a pole at the origin and two pairs of poles on the imaginary axis. In addition, we clarify the parameterization of all extended semi-strongly stabilizable plants and of all extended semi-strongly stabilizing controllers for extended semi-strongly stabilizable plants.