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The risk-sensitive index and theH 2 andH ∞, norms for nonlinear systems

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Abstract

In this paper we study two measures of the “size” of systems, namely, the so-calledH 2 and H∞ norms. These measures are important tools for determining the influence of disturbances on performance. We show that the risk-sensitive index on an infinite time horizon contains detailed information concerning these measures, via small noise and small risk limits.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, Rhode Island, USA

    W. H. Fleming

  2. Department of Engineering, Faculty of Engineering and Information Technology, Australian National University, 0200, Canberra, ACT, Australia

    M. R. James

Authors
  1. W. H. Fleming
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  2. M. R. James
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Additional information

The authors wish to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centres Program. The first author was partially supported by AFOSR F49620-92-J-0081, ARO DAAL03-92-G-0115, and NSF DMS-9300048.

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Fleming, W.H., James, M.R. The risk-sensitive index and theH 2 andH ∞, norms for nonlinear systems. Math. Control Signal Systems 8, 199–221 (1995). https://doi.org/10.1007/BF01211859

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  • DOI: https://doi.org/10.1007/BF01211859

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