報告題目（Title）：Developed Partial-Integral Equation (PIE) Representation of Time-Delay Systems (TDS)
報告人：Matthew M. Peet
報告人單位：Arizona State University, US
報告人簡介：Matthew Peet is an Associate Professor at Arizona State University. He received B.Sci. degrees in Physics and in Aerospace Engineering from the University of Texas at Austin in 1999 and the M.Sci. and Ph.D. degrees in Aeronautics and Astronautics from Stanford University in 2006. He was a Postdoctoral Fellow at INRIA from 2006-2008. From 2008-2012 he was an Assistant Professor of Aerospace Engineering at the Illinois Institute of Technology. He has been with Arizona State University (ASU) since 2012 in the Department of Mechanical and Aerospace Engineering. Prof. Peet has worked extensively on LMI and SOS methods, with over 80 publications in this area, including the first publications on SOS for both delayed and PDE systems.
In this talk, he will present the recently developed Partial-Integral Equation (PIE) Representation of Time-Delay Systems (TDS). Specifically, the PIE framework is an algebraic representation of the delay system which allows us to generalize LMIs developed for Ordinary Differential Equations (ODEs) to Time-Delay Systems without the use of Jensen’s inequality, Wirtinger’sInequality, integration by parts, or any of the commonly used techniques for analysis of Time-Delay Systems.
First the PIE representation of a TDS and the associated operator algebraare present, with associated Matlab implementation. Then it is shown how to transform the LMI for H-infty gain into an operator inequality which is solved using our recently developed Matlab toolbox. Next, LMIfor H-infty optimal Controller Synthesis and optimal observer synthesis are converted into an operator Inequality,respectivelyand the corresponding implementation numerically are demonstrated. Finally, observers and controllers are combined into a dynamic output-feedback controller design and simulate the results.