Computation of the nearest structured matrix triplet with common null space

09/13/2021
by   Nicola Guglielmi, et al.
0

We study computational methods for computing the distance to singularity, the distance to the nearest high index problem, and the distance to instability for linear differential-algebraic systems (DAEs) with dissipative Hamiltonian structure. While for general unstructured DAEs the characterization of these distances is very difficult, and partially open, it has been recently shown that for dissipative Hamiltonian systems and related matrix pencils there exist explicit characterizations. We will use these characterizations for the development of computational methods to compute these distances via methods that follow the flow of a differential equation converging to the smallest perturbation that destroys the property of regularity, index one or stability.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/24/2020

Distance problems for dissipative Hamiltonian systems and related matrix polynomials

We study the characterization of several distance problems for linear di...
research
05/26/2020

Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems

In this paper we discuss Stochastic Differential-Algebraic Equations (SD...
research
02/05/2022

Solving matrix nearness problems via Hamiltonian systems, matrix factorization, and optimization

In these lectures notes, we review our recent works addressing various p...
research
10/13/2019

Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems

We examine interpolatory model reduction methods that are well-suited fo...
research
10/29/2020

A passivation algorithm for linear time-invariant systems

We propose and study an algorithm for computing a nearest passive system...
research
03/13/2020

Finding the closest normal structured matrix

Given a structured matrix A we study the problem of finding the closest ...
research
03/10/2022

Computing Whittle (and Gittins) Index in Subcubic Time

Whittle index is a generalization of Gittins index that provides very ef...

Please sign up or login with your details

Forgot password? Click here to reset