Finite dimensional controller design via the largest robust stability radius

Abstract

Consideration is given to the space of transfer matrices with entries in the quotient field of H-infinity, in which the gap metric is defined. The largest robust stability radius of a transfer matrix is defined as the radius of the largest ball centered at the transfer matrix which can be stabilized by a single controller. There are two schemes presented for designing finite dimensional stabilizing controllers by means of the largest robust stability radius. Both schemes guarantee that the finite dimensional controllers stabilize the original infinite dimensional system. Moreover, the closed-loop response can be estimated.<>