Convex sufficient conditions on asymptotic stability and ℓ2 gain performance for uncertain discrete‐time switched linear systems. Issue 3 (1st February 2014)

• Record Type: Journal Article
• Authors: Xiang, Weiming; Xiao, Jian
• Is Part Of: IET control theory & applications. Volume 8:Issue 3(2014)
• Page Start: 211
• Page End: 218
• Publication Date: 2014-02-01
• Subjects: asymptotic stability -- control system synthesis -- discrete time systems -- H∞ control -- linear systems -- Lyapunov methods -- matrix algebra -- state feedback -- time‐varying systems -- uncertain systems; convex sufficient conditions -- asymptotic stability -- uncertain discrete‐time switched linear systems -- disturbance attenuation property -- dwell‐time dependent Lyapunov function -- DTDLF approach -- â„"2 gain analysis problems -- system matrices -- ℋ∞ control problem -- state‐feedback controllers -- switching law design -- one‐step method -- control synthesis process; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2013.0409
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : In this brief article, the stability and disturbance attenuation property in the sense of ℓ2 gain for switched linear discrete‐time systems are investigated. The computation of ℓ2 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 ℓ2 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.