Synthesis of suboptimal H∞ controllers over a finite horizon

In this paper a finite horizon H∞ optimal control problem is posed and solved. It is shown by way of examples that the finite horizon performance is useful for the fast computation of the infimal H∞ norm in the infinite interval case. Also, a differential equation is derived for the measure of performance. A general suboptimal control problem is then posed and an expression for a suboptimal controller is derived solving the saddle point conditions. An expression for a feedback controller can be derived by solving a dynamic Riccati equation. In the time-invariant case, the finite horizon controller converges to a static controller as the final time becomes large. Examples are given to illustrate the usefulness of the theory.