Partial eigenstructure assignment problem and its application to the constrained linear problem

Abstract

This article presents a new partial eigenstructure assignment method. This technique keeps the open-loop stable eigenvalues and the corresponding eigenspace unchanged. The remaining undesirable eigenvalues are replaced by other chosen values. This methodology is easy and permits to overcome some limitations encountered in the previous methods. Furthermore, our method is applied to solve the constrained control problem for linear invariants continuous-time systems. Indeed, the problem of finding a stabilising regulator matrix gain taking into account the asymmetrical control constraints is transformed to a Sylvester equation resolution. Examples are given to illustrate the obtained results.

Keywords:

• linear systems
• partial eigenstructure assignment
• asymmetrical input constraints