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- and - Low-Gain Feedback: Their Properties, Characterizations and Applications in Constrained Control | IEEE Journals & Magazine | IEEE Xplore

L_{\infty} and L_{2} Low-Gain Feedback: Their Properties, Characterizations and Applications in Constrained Control


Abstract:

Low-gain feedback has found several applications in constrained control, robust control, and nonlinear control. In this paper, we first generalize the existing low-gain d...Show More

Abstract:

Low-gain feedback has found several applications in constrained control, robust control, and nonlinear control. In this paper, we first generalize the existing low-gain design methods by introducing the notion of L-vanishment and by providing a full characterization of feedback gains that achieve such a property. We observe that L low-gain feedback can lead to energy peaking, namely, the control energy required by L low-gain feedback increases toward infinity as the low-gain parameter decreases to zero. Motivated by this observation, we consider the notion of L2-vanishment and establish several of its characterizations, based on which a new design approach referred to as the L2 low-gain feedback approach for linear systems is developed. Different from the L low-gain feedback, the L2 low-gain feedback is instrumental in the control of systems with control energy constraints. As an application of L2 low-gain feedback, the problem of semiglobal stabilization of linear systems with control energy constraints is solved in this paper. The notions of L and L2-vanishment also allow us to establish a systematic approach to the design of L and L2 low-gain feedback. The advantage of this new design approach is that it results in a family of control laws, including those resulting from the existing design methods.
Published in: IEEE Transactions on Automatic Control ( Volume: 56, Issue: 5, May 2011)
Page(s): 1030 - 1045
Date of Publication: 07 September 2010

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