Robust eigenvalue assignment for time-delay systems

Abstract

We consider the problem of robust pole assignment for a linear time invariant plant with state feedback subject to time delay 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 closed-loop eigenvalues to the time-delay system. Secondly we consider systems subject to small input time delays and introduce an unconstrained optimisation algorithm for the computation of a state feedback matrix to deliver the desired pole placement in a manner that minimises the sensitivity of the eigenvalues to input time delays. The performance of the algorithm is compared against an alternative robust pole place..