Disturbance Decoupling with Static Output Feedback

Abstract

The problem of disturbance decoupling with or without internal stability by either state or measurement feedback is well known and has been extensively discussed in the literature for the last three decades. It can be stated as the problem of finding a feedback controller such that the closed-loop transfer function from the disturbance input to the controlled output is zero at all frequencies. This problem actually motivated the development of the geometric approach to linear systems, and has played a key role in a number of problems, such as decentralized control, noninteracting control, model reference tracking control, H ₂ optimal control and H _∞ optimal control. The problem of disturbance decoupling with state feedback (DDP) was solved by Basile and Marro [9] and Wonham and Morse [155], and the problem of disturbance decoupling with dynamic measurement feedback (DDPM) was solved by Akashi and Imai [1] and Schumacher [126]. Furthermore, the problems of disturbance decoupling with state feedback and internal stability (DDPS) and with dynamic measurement feedback and internal stability (DDPMS) were, respectively, solved by Morse and Wonham [101], Wonham and Morse [155], Imai and Akashi [69] and Willems and Commault [153].