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JOURNALS // Avtomatika i Telemekhanika // Archive

Avtomat. i Telemekh., 2025 Issue 2, Pages 21–46 (Mi at16480)

Nonlinear Systems

Towards computation of surface area of Schur stability domain

M. V. Kukoverov

Moscow Integrated Power Company, Moscow, Russia

Abstract: The paper considers the subset of the Schur stability domain, namely, the set of parameters for which the roots of polynomials of degree $n$ lie in the complex unit disc and are real numbers. The method for computation of the hypersurface area of this defined set in $n$-dimensional space is obtained. The maximum surface area of this set is reached for $n=3$, i.e., $3$-dimensional set has maximum surface area.

Keywords: multiple integrals, Schur stability domain, autoregression, stationary autoregressive processes, unit root processes

Presented by the member of Editorial Board: A. I. Malikov

Received: 07.02.2024
Revised: 11.11.2024
Accepted: 25.11.2024

DOI: 10.31857/S0005231025020024


 English version:
Automation and Remote Control, 2025, 86:2, 113–133


© Steklov Math. Inst. of RAS, 2026