An Extension of the Argument Principle and Nyquist Criterion to a Class of Systems With Unbounded Generators

The Nyquist stability criterion is generalized to systems where the open-loop system has infinite-dimensional input and output spaces and an unbounded infinitesimal generator. The infinitesimal generator is assumed to be a sectorial operator with trace-class resolvent. The main result is obtained through use of the perturbation determinant and an extension of the argument principle to infinitesimal generators with trace-class resolvents.