The parameterization of all extended semi-strongly stabilizing controllers

A strong 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. However, when a strongly stabilizing controller is used, steady-state error remains when step disturbances and uncertainties exist in the control system because the strongly stabilizing controllers do not have a pole on the origin. To solve this problem, Hoshikawa et al. define semi-strongly stabilizing controllers that have a pole on the origin and rest of the poles in the open left half plane. In addition, they clarify the parameterizations of all semi-strongly stabilizable plants and all semi -strongly stabilizing controllers for the strongly stabilizable plants. However, the method of Hoshikawa et al. fails to place the poles on the imaginary axis. Some control methods need to place poles on the imaginary axis; for example, the control systems follow si-nusoidal signals and the self-repairing control systems with faulty sensors. To overcome this problem, we expand the results by Hoshikawa et al. and define extended semi-strongly stabilizing controllers. In addition, the parameterizations of all extended semi-strongly stabilizable plants and all extended semi-strongly stabilizing controllers for extended semi -strongly stabilizable plants are clarified.