The H/sub ∞/ index of normal transfer function matrices

Abstract

In the H/sub /spl infin// approach to the design of robust control systems, the H/sub /spl infin// norm of certain weighted transfer function matrices of a control system is an important index of system robustness. The design procedure of a robust control system is essentially a procedure of minimizing that H/sub /spl infin// norm index. This paper proves that the normality of certain transfer function matrices of a control system is a sufficient condition for minimum H/sub /spl infin// index. Moreover, for the 2-input 2-output case, it is not only sufficient, but also necessary. Thus, the normalization of certain transfer function matrices of a system guarantees the best system robustness property in the sense of minimum H/sub /spl infin// index. This serves as the basis of a new approach to robust control system design-the optimization of parametrized normal matrix (OPNORM) method. It is also shown here that the weighting function in the H/sub /spl infin// norm index has certain interesting significance in the design of open-loop system eigenloci. >