Upper bounds on the induced norm of the input/output operators in linear systems with L2 input and output signals, are provided. The main idea is to transform the original problem into a parametized set of indefinite LQ optimization problems. Using the classical maximum principle, the existence of solutions to the latter is equivalent to the solvability of a boundary value hamiltonian system or, equivalenty, of an ‘indefinite’ Riccati equation. Our time domain approach enables the treatment of a very general linear set-up, including time-varying, infinite-dimensional, finite- and infinite-horizon systems.
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Gilead Tadmor (1990) studied this question.
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