Poor convergence in applying an optimal integral regulator to a system with a RHS zero

Necessary and sufficient conditions of the optimal regulator incorporating integral feedback were given by Porter Ill and Smith and Davison [2]. This note presents a problem of poor convergence in an iterative solution of the discrete Riccati equations when an optimal regulator incorporating
r = m
integral feedback is applied to a system which has a zero on the RHS of
s
-plane, where
r
and
m
are the input and output dimensions, respectively. The problem of poor convergence was clarified by simulation studies and analytically examined based on certain assumptions. The poor convergence is due to poor choice of an initial guess in the above special situation. However, this problem is very important from a practical point of view because the initial guess is difficult in the first stage of regulator design.