A Small Gain Approach for Stability Analysis of Systems with Random Time-varying Delays

Recent advances in broad fields of science and engineering brought forth new issues and challenges to the area of time-delay systems. Delays in communication networks and biological systems, for example, have been found to play a critical role in the system behavior and toward system performance. While understanding delay effects has risen to be ever more important and is gaining visible research attention, existing tools for analysis and design of time-delay systems fail to address the new issues, which are exemplified by difficulties imposed by random, time-varying, and multi-scaled delays. This project is intended to answer to these challenges and needs. Built on the PI’s research strength and success in the area, we seek to develop a small-gain analysis approach for systems subject to random, time-varying, and multi-scaled delays, which consist of initiatives in developing 1) small-gain input-output stability criteria, 2) modeling and approximation techniques for time-varying, random delays, 3) efficient stability tests and computational algorithms, and 4) potential applications to delay problems found in communication networks and biological systems. The project is believed to have the potential to impact theoretical and applied research in a broad range of scientific and engineering areas, including the fields of systems and control, communications, and biological systems studies.