On the mixed sensitivity H∞ control problem with poles on the imaginary axis

This paper presents a simple methodology for building the generalized plant for the mixed sensitivity H∞ control problem, where the control object and the weighting functions for the sensitivity function may have poles on the imaginary axis. Our methodology shows that the ordinary assumptions made in the standard H∞ design are briefly satisfied in spite of the existence of poles on the imaginary axis, and the stabilizability and the detectability of (A, B2, C2) are determined by the characteristic of the control object. So this methodology makes it possible to use the standard method to solve the H∞ design problem for an oscillatory system or a servo system. An example is given to illustrate the results.