Eigenvalue Structure of the Predictor Feedback for Discrete-time LTI Systems
Lorlynn Asuncion Mateo (1251127)
The discrete-time predictor feedback system was designed to compensate for constant input delays based on d-step ahead state predictions in discrete-time linear time-invariant systems. The entire spectrum, initially investigated by numerical computation, shows that aside from the eigenvalues of A+BK, there are other eigenvalues located about the origin. Existing literature only focuses on the spectrum coinciding with that of A+BK, but, in this study, we extended previous results by considering the full state of the system to obtain the eigenvalues mathematically. In contrast to the continuous-time case, it is important to note that the discrete-time delay system is finite-dimensional. From this viewpoint, we started our analysis from the state space representation to construct a proof that derives the poles of the closed-loop system. Furthermore, as a preliminary step, we attempt a frequency domain analysis by considering non-zero initial conditions in taking the Z-transform of the system with an example. After studying the example with smaller length delay, we proceed to construct a generalized proof for deriving the eigenvalues of the discrete-time predictor feedback system in frequency domain.