Optimization estimates of dynamical system characteristics
type: Item
instance of: scholarly article
zbMATH Open document ID: 0976.49013
author: O. I. Stadnik
author: V. F. Davydov
author: Denis Khusainov
publication date: 2001-09-16T00:00:00Z
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 37N35
zbMATH DE Number: 1646421
zbMATH Keywords: optimization
zbMATH Keywords: estimates
zbMATH Keywords: dynamical system characteristics
zbMATH Keywords: Lyapunov function
zbMATH Keywords: necessary and sufficient conditions of optimality
MaRDI profile type: Publication
title: Optimization estimates of dynamical system characteristics
published in: Zhurnal Obchyslyuval'noïta Prykladnoï Matematyky
review text: The problem of finding the best estimates for the transition characteristics is reduced to the optimization problem NEWLINE\[NEWLINE H_0= \text{arg inf} _{H \in Z [H ]} \{\phi [ \lambda _{\min} (G[ H]), \lambda_{\max} (G[ H]) ]\}, NEWLINE\]NEWLINE where \(\lambda _{\min} (\cdot), \lambda _{\max}(\cdot)\) are the minimal and maximal characteristic numbers of symmetric positive definite matrices, respectively, \(G[ H]\) is a linear matrix operator, \(\phi[\cdot,\cdot]\) is a continuously differentiable function, \(Z[H]\) is a set of positive definite matrices. The authors prove the existence of a solution of the considered optimization problem, obtain the necessary and sufficient conditions of optimality in a particular case and apply these results to the construction of estimates of the asymptotic stability domain for a system of differential equations with quadratic right sides.
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1646421