Negative imaginary functions for infinite dimensional systems

This paper studies the operator-valued irrational complex symmetric negative imaginary (CSNI) systems. The complex symmetric negative imaginary function is defined using the complex symmetric operator. In this case, a matrix-valued symmetric negative imaginary transfer function G(s) : C -> C-mxm is identical to an operator-valued CSNI transfer function defined on a finite dimensional Hilbert space. A necessary and sufficient condition for operator-valued CSNI transfer functions is given by using the frequency-domain properties. A specific illustration of an operator-valued CSNI function is shown.