Quadratic separation framework for stability analysis of a class of systems with time delays

This paper is concerned with the stability analysis of a class of systems with time delays through a kind of Quadratic Separation (QS) Framework. A novel method for the construction of Integral Quadratic Constraints (IQCs) that will be used in the QS framework is proposed. A unified framework is proposed based on the QS theory and the Lyapunov theory, and then is applied to the stability analysis of linear systems with time delays. Stability criteria are established based on the proposed approach. Numerical examples are finally provided to show its effectiveness.