Generalized Nyquist criterion of continuous-time periodic systems and its implementation (I): theoretic results

This paper is divided into two parts. In the first part, we establish a generalized Nyquist stability criterion to finite-dimensional linear continuous-time periodic systems by means of the 2-regularized determinants about the harmonic transfer operator, which is a Hilbert-Schmidt operator. The generalized Nyquist stability criterion can apply to most practical periodically time-varying continuous-time systems with standard assumptions about the system matrices.