Open AccessKronecker weights for instability analysis of Markov jump linear systems
Author(s) -
Mei Wenjie,
Ogura Masaki
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5506
Subject(s) - kronecker delta , markov chain , mathematics , affine transformation , instability , linear system , jump , matrix (chemical analysis) , markov process , mathematical optimization , control theory (sociology) , computer science , statistics , mathematical analysis , artificial intelligence , physics , materials science , control (management) , quantum mechanics , mechanics , pure mathematics , composite material
In this study, the authors analyse the instability of continuous‐time Markov jump linear systems. Although there exist several effective criteria for the stability of Markov jump linear systems, there is a lack of methodologies for verifying their instability. In this study, they present a novel criterion for the exponential mean instability of Markov jump linear systems. The main tool of the authors' analysis is an auxiliary Markov jump linear system, which results from taking the Kronecker products of the given system matrices and a set of appropriate matrix weights. They show that the problem of finding matrix weights for tighter instability analysis can be transformed into the spectral optimisation problem on an affine matrix family, which can be efficiently solved by gradient‐based non‐smooth optimisation algorithms. They confirm the effectiveness of the proposed methods by numerical examples.