On the stabilization of linear systems

Abstract

be stabilizable. Here A is an n by n matrix, x and b are n by 1 column matrices (or vectors), p is a 1 by n row matrix and q and u are scalars. We shall assume that the elements of all these may be complex numbers. The vector x can be interpreted physically as the output of a linear system characterized by the matrix A. The vector b corresponds to some feedback or control mechanism with u the controlling signal and p and q adjustable parameters in the controlling circuit. Romanenko calls the system (A, b) stabilizable if for any nonempty set S of n+1 or less complex numbers there exist p and q such that