Strong stabilization of high order plants

Abstract

Designing stable feedback controllers that stabilize a given plant, known as strong stabilization, has been explored in the literature by using several algorithmic construction procedures. Many of these methods rely on step-by-step interpolation or solving an auxiliary H∞ control problem, or a set of LMIs. This paper gives an explicit construction of simple strongly stabilizing controllers for plants that have restrictive number of zeros in the extended right half plane, without any restrictions on the number or location of poles. A similar construction is also developed for the case of plants with restrictions on the poles. The order of the proposed stable controllers is at most one less than that of the plant, and they are computed by selecting just a few positive parameters determined from the H∞ norms of certain transfer functions.