Localization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matrix

Ahsani Tehrani, H.

Localization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matrix

Document Type : Original Research Articles

Author

H. Ahsani Tehrani

Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrood University, Shahrood, Islamic Republic of Iran

Abstract

This paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center and radius. This new algorithm can also be used for the placement of closed-loop eigenvalues in a specified disc in z-plane for discrete-time linear systems. Some illustrative examples are presented to show the advantages of this new technique.

Keywords

Discrete-time systems

State feedback matrix

Localization of eigenvalues

Disc

Closed-loop system