Nyquist Stability Criterion for Sampled-Data Systems Based on the 2-Regularized Determinant and Robust Internal Stability Analysis

Abstract

In this paper, we first extend the Nyquist stability criterion for sampled-data systems based on the 2-regularized determinant pertinent to Hilbert-Schmidt operators in such a way that the continuous-time generalized plant is allowed to have a direct feedthrough term from the disturbance input to the controlled output. By means of this Nyquist stability criterion, we derive robust internal stability theorems of sampled-data systems such as the small gain theorem and the passivity theorem.