Time delays arise in the transport of energy, mass, information and such, and are omnipresent in natural and engineered systems. Modern interconnected networks are especially prone and indeed, are vulnerable to long and variable delays; systems and networks in this category are many, ranging from communication networks, sensor networks, cyber-physical systems, to biological systems. Except on rare instances, time delays are likely to result in degraded performance, poor robustness, and even instability, which consequently pose significant challenges to the analysis and design of control systems under delayed feedback.
While a recurring subject of study, over the last two decades or so there have been particularly notable advances in the stability analysis of time delay systems, thanks to the development of analysis methods drawing upon robust control theory, and the development of computational methods in solving linear matrix inequality (LMI) problems. An extraordinary volume of the literature is in existence on stability problems, and various time- and frequency-domain stability criteria have been developed. Of these developments, while an overwhelming majority of the available results are obtained based upon time-domain Lyapunov-Krasovskii methods and require the solution of LMIs, frequency-domain conditions in the spirit of small-gain theorem have also been sought after. Generally, time-domain stability conditions are applicable to both constant and time-varying delays, but are known to suffer from a varying degree of conservatism. In contrast, frequency-domain tests are largely restricted to constant delays though often provide tight conditions and appear more susceptible to feedback synthesis.
Despite the considerable advances on stability analysis, control design problems for time-delay systems prove far more challenging. Feedback stabilization of time-delay systems poses a difficult problem and has been somewhat an underdeveloped research area. Fundamental robustness issues have been seldom investigated as well. Furthermore, recent advances in broad fields of science and engineering brought forth new issues and problems to the area of time-delay systems; time delays resulted from the interconnected systems and networks present new challenges unexplored in the past and are increasingly seen to have far more grave effects, which the existing theories do not seem to be well equipped with.
In the workshop we intend to discuss a wide variety of subjects on the stability and stabilization of time-delay systems. We ask such questions as when will a delay system be stable or unstable, and for what values of delay? When can an unstable delay system be stabilized? What range of delay can a feedback system tolerate to maintain stability? Fundamental questions of this kind have long eluded engineers and mathematicians alike, yet ceaselessly invite new thoughts and solutions. We shall present tools and techniques that answer to these questions, seeking to provide exact and efficient computational solutions to stability and stabilization problems of time-delay systems. In particular, we shall develop in full an operator-theoretic approach that departs from both the classical algebraic and the contemporary LMI solution approaches, notable for both its conceptual appeal and its computational efficiency. Extensions to networked control and multi-agent systems will also be addressed.