New relations between norms of system transfer functions

作者：Ivanov Tzvetan^*; Anderson Brian D O; Absil P A; Gevers Michel

来源：Systems & Control Letters, 2011, 60(3): 151-155.

DOI：10.1016/j.sysconle.2010.10.008

• Robust control
• LQR
• Confidence region
• Covariance
• Weighted H(2) norm
• Supremum norm
• H(infinity) norm
• Tight bound
• Reproducing kernel

It is well-known that the H(2)-norm and H(infinity)-norm of a transfer function can differ arbitrarily since both norms reflect fundamentally different properties. However, if the pole structure of the transfer function is known it is possible to bound the H(infinity)-norm from above by a constant multiple of the H(2)-norm. It is desirable to compute this constant as tightly as possible. In this article we derive a tight bound for the H H(infinity)-norm given knowledge of the H(2)-norm and the poles of a transfer function. We compute the bound in closed form for multiple input multiple output transfer functions in continuous and discrete time. Furthermore we derive a general procedure to compute the bound given a weighted L(2)-norm.

• 出版日期2011-3