Eigenvalue assignment for systems with multiple time-delays

Abstract

We consider the problem of pole assignment for a linear time invariant plant with state feedback subject to multiple time delays in the control input. For systems with a known time delay, we offer a parametric formula for the feedback gain matrix that will assign a desired set of closedloop eigenvalues to the time-delay system. We consider some well-established pole placement methods for systems without delay that utilise pole placement via state feedback in order to achieve their desired performance objective. We explore the extent to which their desired control performance objective may be successfully achieved for a time-delay system by placing the primary poles of the delayed system at the same locations as for the system without delay. The role of the secondary poles of the time-delay system will also be investigated since they are known to affect both the stability and performance.