Open AccessDrazin inverse conditions for positivity and stability of switched descriptor systems
Author(s) -
Ding Xiuyong,
Zhai Guisheng,
Liu Xiu
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.2018.5253
Subject(s) - drazin inverse , mathematics , stability (learning theory) , set (abstract data type) , inverse , matrix (chemical analysis) , consistency (knowledge bases) , projector , linear matrix inequality , linear system , state (computer science) , control theory (sociology) , linear programming , decomposition , mathematical optimization , algorithm , computer science , discrete mathematics , artificial intelligence , mathematical analysis , ecology , materials science , geometry , control (management) , machine learning , composite material , biology , programming language
This study provides an alternative approach to stability analysis of positive switched descriptor systems (SDSs). First, by introducing a Drazin‐inverse‐based projector which takes a simpler form than the traditional matrix‐decomposition‐based ones, the state consistency of SDSs is guaranteed. Then, regarding the fact that SDSs may not be positive even if all individual subsystems are positive, two different definitions of positivity are introduced and a complete characterisation is provided. The stability issue is also addressed and two checkable approaches are proposed, which are formulated as a set of linear matrix inequality problems and linear programming problems, respectively.