Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems. (May 2017)

• Record Type: Journal Article
• Authors: Briat, Corentin
• Is Part Of: Nonlinear analysis. Volume 24(2017)
• Page Start: 198
• Page End: 226
• Publication Date: 2017-05
• Subjects: Positive systems -- Impulsive systems -- Switched systems -- Clock-dependent conditions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2017.01.004
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise decrease of a linear copositive Lyapunov function and are formulated in terms of finite-dimensional or semi-infinite linear programs. To be applicable to uncertain systems and to control design, a lifting approach introducing a clock-variable is then considered in order to make the conditions affine in the matrices of the system. The resulting stability and stabilization conditions are stated as infinite-dimensional linear programs for which three asymptotically exact computational methods are proposed and compared with each other on numerical examples. Similar results are then obtained for linear positive switched systems by exploiting the possibility of reformulating a switched system as an impulsive system. Some existing stability conditions are retrieved and extended to stabilization using the proposed lifting approach. Several examples are finally given for illustration.