Input-output passive framework for delay systems

Multivariable linear systems with several delays are considered. Delays are allowed in the state as well as in the input or the output. Passivity and dissipativity of such systems are considered both in the input-output and state space framework in connection with hyperstability. In the input-output framework necessary and sufficient conditions of passivity and hyperstability of delay systems are given in the language of positive real functions. Furthermore, necessary and sufficient conditions for positive realness are derived for a class of meromorphic functions describing delay systems.