Analytical Stability Conditions on Interconnected Nonlinear Systems With Delays

Abstract

This paper is concerned with stability of interconnected systems with time delays. We develop a self-contained approach to stability analysis for linear and nonlinear systems in a unified framework. New lemmas are established on matrix properties and used as the key to make negativity of the derivative of the Lyapunov function. The scalar and simple analytical stability conditions are given. Unlike the majority of the literature on stability of delay systems, no matrix equations/inequalities are involved in our conditions, which is true even for large-scale systems and nonlinear subsystems with delayed interconnections. They are applicable to the more general nonlinear, time-varying, and/or interconnected systems than the relevant results reported in the literature. The examples are presented for illustration of the new results.

Keywords

• Stability
• interconnected systems
• time delay
• Lur’e Postnikov
• arrow form matrix
• aggregation technique