# Subspace Method for Approximation of H-infinity Norms of Large-Scale Control Systems

**Dr. Nicat Aliyev **

Baku Higher Oil School

**Abstract: **We are concerned with the computation of the H-infinity norm for H-infinity functions of the form H(s) = C(s)D(s)^-1B(s), where the middle factor is the inverse of an analytic matrix-valued function, and C(s), B(s) are analytic functions mapping to short-and-fat and tall- and-skinny matrices, respectively. For instance, transfer functions of descriptor and delay systems fall into this family. We focus on the case where the middle factor is huge. We propose a subspace projection method to obtain approximations of the function H where the middle factor is of a much smaller dimension. The H-infinity norms are computed for the resulting reduced functions, then the subspaces are refined by means of the optimal points on the imaginary axis where the largest singular value of the reduced function is maximized. The subspace method is designed so that certain Hermite interpolation properties hold between the largest singular values of the original and reduced functions. This leads to a superlinearly convergent algorithm with respect to the subspace dimension, which we prove and illustrate on various numerical examples.

**Speaker Biography: **Dr Nicat Aliyev graduated from Dokuz Eylul University’s Department of Mathematics in 2008. In 2011, he completed his master’s in financial mathematics with a dissertation related to Barrier Option Pricing. Dr. Nicat Aliyev received his PhD in January 2018 from Koç University, Istanbul. During his PhD studies in 2017, he visited the Max Planck Institute in Magdeburg for six months (he joined the research group of Prof. Peter Benner) and Berlin TU for one week as a visiting researcher. After his PhD, he started to work as an assistant professor at Istanbul Zaim University. Then, he moved back to his home country, Azerbaijan, and in 2019 began to work as a research scientist at Azerbaijan National Academy of Sciences, Institute of Mathematics and Mechanics in Baku, Azerbaijan. In September 2020, he worked as an assistant professor at the University of Fench Azerbaijan. From January 2021 to December 2021, he worked as a postdoctoral research scientist at Charles University, Department of Numerical Mathematics. From January 2022 to December 2023, he worked as a research scientist at Czech Technical University. Currently, he works as a math teacher at Baku Higher Oil School. So far, he taught several mathematics and related courses, such as calculus, linear algebra, mathematical modeling, robust control, probability and statistics, numerical methods, machine learning, data visualization, etc. His main research interests include eigenvalue optimization, numerical methods for optimization, control theory, model reduction, and machine learning.

**Meeting ID: **389 210 781 240

**Password: **8hK5Wy