Section: New Results
Stable Controller for Infinite-dimensional systems
The controllers, besides the stabilization, are often designed to achieve some performance and robustness objectives by minimizing 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 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 norm constraints. Then, by utilizing this result, stable controller design method are presented.