Another look at finite horizon H∞ control problems for systems with input delays

Abstract

We discuss a finite horizon H ∞ control problem for time-varying systems with input delays. Clarifying a relationship between two H ∞ control problems in input delay case and in measurement delay case, we derive a solution in input delay case based on the known result for the H ∞ control problem in measurement delay case, and show that the solution has the same predictor–observer structure as the solution in measurement delay case has. Using this structural information on the solution, we also present an elementary proof of the solution to the finite horizon H ∞ control problem for systems with input delays, which is based only on completion of squares.