H-infinity-norm and invariant manifolds of systems with state delays

The problem of finding bounds on the H-infinity-norm of systems with a fini te number of point delays and distributed delay is considered. Sufficient c onditions for the system to possess an H-infinity-norm which is less or equ al to a prescribed bound are obtained in terms of Riccati partial different ial equations (RPDE's). We show that the existence of a solution to the RPD E's is equivalent to the existence of a stable manifold of the associated H amiltonian system. For small delays the existence of the stable manifold is equivalent to the existence of a stable manifold of the ordinary different ial equations that govern the flow on the slow manifold of the Hamiltonian system. This leads to an algebraic, finite-dimensional, criterion for syste ms with small delays. (C) 1999 Elsevier Science B.V. All rights reserved.