Abstract
The problems studied in this note have been motivated by our work in generalizing linearH ∞ control theory to nonlinear systems. These ideas have led to a design procedure applicable to analytic nonlinear plants. Our technique is a generalization of the linearH ∞ theory. In contrast to previous work on this topic ([9], [10]), we now are able to explicitly incorporate a causality constraint into the theory. In fact, we show that it is possible to reduce a causal optimal design problem (for nonlinear systems) to a classical interpolation problem solvable by the commutant lifting theorem [8]. Here we present the complete operator theoretical background of our research together with a short control theoretical motivation.
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This work was supported in part by grants from the Research Fund of Indiana University, the National Science Foundation DMS-8811084 and ECS-9122106, by the Air Force Office of Scientific Research F49620-94-1-0098DEF, and by the Army Research Office DAAL03-91-G-0019 and DAAH04-93-G-0332
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Foias, C., Gu, C. & Tannenbaum, A. Nonlinearity inH ∞-control theory, causality in the commutant lifting theorem, and extension of intertwining operators. Integr equ oper theory 23, 89–100 (1995). https://doi.org/10.1007/BF01261204
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DOI: https://doi.org/10.1007/BF01261204