Neutral Type Linear Functional Differential Equations Stability Study

The systematic research of FDE began in 1850s.FDE and DDE have been extensively developed since 1959, and each branch has been set up a complete theory system. Now, more and more scholars study FDE and explore further developments. Neutral and linear functional differential equation are the parts of great interest to people.NDEs have the properties that are similar in some aspect to the properties of ordinary difference equations and in the other aspects are similar to the properties of functional differential equations. This duality of NDE is essential for a study of asymptotic behaviour of their solutions.This paper mainly includes five parts:1. I present the criteria of the NDE through the characteristic polynomial of the NDE Two examples are given to illustrate advantages of the criteria.2. Some new and simple explicit conditions in terms of the structured singular value are provided to ensure the stability of the interval system. Example is given to demonstrate the validity of our criteria.3. Some new delay-independent stability and robust stability criteria, which are simpler and less conservative than existing results, of general neutral type descriptor system are considered. The criteria derived in terms of linear matrix inequalities(LMIs) and the stability of the operator4. Based on the generalized Gersgorin theorem, several new delay-independent sufficient...