Robustness analysis for a class of linear neutral systems in a critical case

This study pays attention to robust stability of a class of uncertain neutral systems in a critical case, where the spectral radius of the principal neutral term (matrix H in this study) is equal to 1. It is shown that usual methods cannot deal with such systems with uncertainties. Thus, a novel method is developed, whose idea is to examine whether or not an existing stability criterion still holds when the uncertainties are sufficiently small. More specifically, it is to examine whether or not the existing stability criterion in terms of a linear matrix inequality (LMI) still has a solution with the sufficiently small uncertainties. By analysing the structure of the solution, a new robust stability criterion is derived in terms of the existence of solutions to an equation. An application shows the effectiveness of the proposed method by dealing with a problem caused by numerical methods when solving LMIs.