H ∞ control with bandwidth and H 2 constraints

This paper discusses some practical issues associated with H ∞ controller design based on the results presented by Doyle, Glover, Khargonekar, and Francis (DGKF). First, the optimal H ∞ controller based on these results is discussed from a practical applications point of view. Then, tradeoffs between the H ∞ norm and other performance characteristics, specifically bandwidth and the H 2 norm, are considered. It is shown through example that when the optimal HH ∞ norm is relaxed by only 10-20 percent and the central controller of DGKF is used, significant benefits in both the controller bandwidth and the H 2 norm of the closed-loop system can be achieved. Furthermore, it is shown that the results for the H 2 /H ∞ tradeoff compare favorably to a controller designed using the mixed H 2 /H ∞ method developed by Bernstein and Haddad, even for the case in which the controlled output associated with the H 2 objective is different from that associated with the H ∞ objective. Thus, it is demonstrated that other performance criteria, such as controller bandwidth and the H 2 norm of the closed-loop system, can be easily used with the results of DGKF to select a desirable suboptimal H ∞ controller.