Invited Speakers

There are time delays not only in natural systems such as electrical systems, biological systems, chemical processes, and social networks, but also in artificial systems such as networks. However, since time-delay systems are infinite dimensional rather than finite dimensional, analytic techniques had hardly handled time-delay systems. This talk will address meaningful numerical techniques for analysis of time delay systems.
In 1999, an integral inequality was introduced that plays a key role in generating the delay-dependent stability condition of time-delay systems in terms of linear matrix inequalities. The integral inequality has two kinds of vectors inside: state-derivative vectors that are a function of the integrant and the other vectors that are not, leading to the construction of a delay-dependent stability condition. This work initiated a new direction in robust control for time delay systems with numerical techniques based on linear matrix inequalities. Whereas the integral inequality lemma played a key role in guiding various delay-dependent criteria for time-delay systems, the Jensen integral inequality had become an alternative as a way of reducing the number of decision variables at the expense of a deterioration in performance. It loosened the integral term of the quadratic quantities directly into the quadratic term of the integral quantities, which lead to a linear combination of positive functions weighted by the inversion of the convex parameters. In 2011, a reciprocal-convexity lower bound lemma was suggested for such a combination, which dramatically increased the performance behavior of the Jensen inequality lemma almost identical to that of the integral inequality lemma, but with much less decision variables. Therefore, this lemma overcame the issue of large computation in the numerical techniques. As an alternative of integral inequalities in 1999, the Jensen integral inequality combined with the reciprocal-convexity lower bound lemma in 2011 became a powerful mathematical tool for stability analysis of time-delay systems. In 2015, a new class of integral inequalities were generated to produce much tighter bounds. When the function is expressed in terms of orthogonal bases, the total energy is the sum of the energy of each component corresponding to the bases. This insight produced multiple-order integral inequalities based on various orthogonal bases.

Biography:
PooGyeon Park received the B.S. and M.S. degrees in control and instrumentation engineering from Seoul National University, Seoul, South Korea, in 1988 and 1990, respectively, and the Ph.D degree in electrical engineering from Stanford University, Stanford, CA, USA, in 1995. Since 1996, he has been affiliated with the division of electrical engineering with the Pohang University of Science and Technology (POSTECH), Pohang, South Korea, where he is currently a Professor. His current research interests include robust control for LPV systems, network systems, time delay systems, fuzzy systems, and multi-agent systems. He won 2020 Korea Engineering Award from the President of the Republic of Korea. He is a member of the Korea Academy of Science and Technology, a Nam-go Chair Professor, a fellow of the Institute of Control, Robotics, and Systems, and the Vice-President for Education of the Asian Control Association.