A Nevanlinna--Pick Approach to Time-Domain Constrained i Control

In this paper, generalized Nevanlinna--Pick theory is used to solve a time-domain constrained $i$ control problem for linear time-invariant discrete-time systems. First it is shown that if constraints are imposed only over a finite horizon (i.e., only on the first $n$ samples), then the problem reduces to a finite-dimensional convex minimization problem. Subsequently it is shown that if these problems are conveniently modified, then letting the horizon length go to infinity produces a solution to the infinite-horizon problem.