Section: New Results

Stable $H_{\infty }$ Controller for Infinite-dimensional systems

The controllers, besides the stabilization, are often designed to achieve some performance and robustness objectives by minimizing $H_{\infty }$ norm of some cost functions. The resulting controller may be stable or unstable. The unstable controllers, however, are more sensitive to sensor/actuator faults, or nonlinearities. It is not an easy task to design a stable controller for systems having infinitely many zeros and poles in the right-half-plane. By using the similar idea in [88] , stable $H_{\infty }$ controller design method will be presented for a certain class of infinite-dimensional plants. The plants may have infinitely many unstable zeros, however, it is assumed that these zeros are unformly separated. Under some certain assumptions, first, a sufficient condition will be presented to construct a real unit function, which satisfies certain interpolation conditions at the right-half-plane zeros of the plant and some $H_{\infty }$ norm constraints. Then, by utilizing this result, stable $H_{\infty }$ controller design method are presented.