Open AccessConvex sufficient conditions on asymptotic stability and ℓ 2 gain performance for uncertain discrete‐time switched linear systems
Author(s) -
Xiang Weiming,
Xiao Jian
Publication year - 2014
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.2013.0409
Subject(s) - dwell time , control theory (sociology) , discrete time and continuous time , exponential stability , lyapunov function , linear system , stability (learning theory) , convex optimization , computation , mathematics , regular polygon , computer science , control (management) , nonlinear system , algorithm , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , machine learning , medicine , clinical psychology , statistics
In this brief article, the stability and disturbance attenuation property in the sense of ℓ 2 gain for switched linear discrete‐time systems are investigated. The computation of ℓ 2 gains against dwell time has been viewed as an open problem so far. A novel dwell‐time dependent Lyapunov function (DTDLF) is introduced to study the stability and ℓ 2 gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, thus it is capable to be generalised to switched systems with uncertainties. Then, as an application, the ℋ ∞ control problem is considered. Based on the DTDLF approach, the control synthesis procedures including state‐feedback controllers and switching law design are unified into one‐step method that explicitly facilitates the control synthesis process. Finally, numerical examples are provided to illustrate the proposed results.