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Output-input stability and minimum-phase nonlinear systems
<span title="">2002</span>
<i title="Institute of Electrical and Electronics Engineers (IEEE)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tiaci7xy45hczhz755zlpu5h7q" style="color: black;">IEEE Transactions on Automatic Control</a>
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<span title="2001-03-26">2001</span>
<span class="release-stage">accepted</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0006133v2">arXiv:math/0006133v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hz7bfxsp6zcgzer46quyetksqu">fatcat:hz7bfxsp6zcgzer46quyetksqu</a> </span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0006133v2">arXiv:math/0006133v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hz7bfxsp6zcgzer46quyetksqu">fatcat:hz7bfxsp6zcgzer46quyetksqu</a> </span>
<span title="2000-06-19">2000</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0006133v1">arXiv:math/0006133v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lf2fdwrbyjg4fgu5okkpz43uom">fatcat:lf2fdwrbyjg4fgu5okkpz43uom</a> </span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0006133v1">arXiv:math/0006133v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lf2fdwrbyjg4fgu5okkpz43uom">fatcat:lf2fdwrbyjg4fgu5okkpz43uom</a> </span>
This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the "input-to-state stability" philosophy, it requires the state and the input of the system to be bounded by a suitable function of
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... e output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of output-input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control.
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