Abstract
The problems studied in this note have been motivated by our work in generalizing linear H ∞ 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 linear H ∞ 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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© 1995 Birkhäuser Verlag Basel/Switzerland
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Foias, C., Gu, C., Tannenbaum, A. (1995). Nonlinearity in H ∞-Control Theory, Causality in the Commutant Lifting Theorem, and Extension of Intertwining Operators. In: Gohberg, I., Langer, H. (eds) Operator Theory and Boundary Eigenvalue Problems. Operator Theory: Advances and Applications, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9106-6_10
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DOI: https://doi.org/10.1007/978-3-0348-9106-6_10
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