On Stable [formula omitted] controller design for plants with infinitely many unstable zeros and poles

Abstract

In this work, stable H∞ controller design problem for linear time-invariant single-input single-output plants, which have infinitely many open-right-half-plane zeros and possibly infinitely many right-half-plane poles, is considered. Interpolation-based approach is developed to solve the problem. The approach requires to construct a unit in H∞ satisfying certain interpolation conditions at the open-right-half-plane zeros of the plant and H∞ norm constraint. In order to construct such a unit function, first, construction of an H∞ function satisfying interpolation conditions at given countably many distinct points in the open-right-half plane is presented. Then, by using the upper bound on the H∞ norm of the constructed function and the small-gain theorem, first, sufficient condition is presented for the solution of the sensitivity minimization problem by a stable controller and design methodology for such a controller is presented. Then, stable H∞ controller design approach for the considered class of plants is presented under certain assumptions. A numerical example is given to verify the presented results.