H∞ norm and slow-fast decomposition of systems with small delay

The problem of finding the H_∞-norm of systems with a finite number of discrete delays and distributed delay is considered. Sufficient conditions for the system to possess an H_∞-norm which is less or equal to a prescribed bound are obtained in terms of the Riccati partial differential equations (RPDE´s). We show that the existence of the solution to the RPDE´s is equivalent to the existence of the stable manifold of the associated Hamiltonian system. The main result of the paper is a derivation of algebraic finite-dimensional criterion for the solvability of RPDE´s for systems with small time-delays. The result is based on slow-fast decomposition of the Hamiltonian system.