Pole assignment of high-order linear systems with high-order time-derivatives in the input

Abstract

This paper studies pole assignment of a class of high-order (HO) linear systems, which contains HO time-derivatives of both the state vector and the input vector, and can be used to model some practical control systems directly. Based on an equivalent first-order linear system, whose state vector contains HO time-derivatives of both the state vector and the input vector of the original HO linear system, it is shown that the pole assignment problem is solvable if and only if solutions to a linear matrix equation, which takes a similar form as the original HO linear system, are such that a matrix is nonsingular. Meanwhile, all the feedback gains are characterized by solutions to the linear matrix equation. Explicit solutions to the linear matrix equations are then proposed by using right-coprime factorization of the original HO linear system. Explicit feedback gains are also established for some special cases. A numerical example is worked out to illustrate the effectiveness of the proposed approach.