Abstract
In this note, we extend the local nonlinear commutant lifting theorem ofJ. Ball, C. Foias, J. W. Helton, and A. Tannenbaum [2,9] to causal input/output operators. This is accomplished by utilizing the causal dilation theory developed by C. Foias and A. Tannenbaum [14] and C. Foias and A. Tannenbaum and the author [10, 11], in order to guarantee the causality of the optimal interpolant derived in the nonlinear framework. This theory is moreover applied to a nonlinear H∞ synthesis problem in robust control.
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Gu, C. (2000). On a Nonlinear Causal Commutant Lifting Theorem. In: Bercovici, H., Foias, C.I. (eds) Operator Theory and Interpolation. Operator Theory Advances and Applications, vol 115. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8422-8_9
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DOI: https://doi.org/10.1007/978-3-0348-8422-8_9
Publisher Name: Birkhäuser, Basel
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