This SGER proposal presents an innovative and unique perspective on a ubiquitous yet unsolved problem: the stability assessment of linear time invariant multiple time delay systems (LTI-MTDS). It entails a systematic procedure resulting in a complete map of the system stability in the domain of the time delays. This paradigm called "the cluster treatment of characteristics roots-CTCR" is built upon two very interesting properties of LTI-MTDS which were unrecognized until the recent work of the PI. The funding is requested for a one-year study on two key directions: (a) To explore the viability of the new procedure for higher order dynamics and higher number of time delays, (b) To introduce a new concept of controlling LTI-MTDS: time-delay scheduling (management). If understood well such a strategy can introduce a powerful tool to the controls designer. The broader impact appears in several categories: Scientific impact: The study covers a very important and basic research topic. The TDS are known to be mathematically very challenging. We suggest a phenomenological perspective, CTCR, to help understand their stability properties. Secondly, the potential utilization of the findings is strong. Some important dynamics are governed by MTDS, such as machine tool chatter in simultaneous machining, the data-network communications and congestion dynamics. Educational impact: The PI will further profit from this research by incorporating some of the findings into his advanced level graduate course 'ME 379 Advances in Control System Design". He has taught this course in Fall 2003 semester already and a part of the syllabus was on TDS stability.
