2016/08/09 by Corentin Briat, Briat, Corentin · 1 citation
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1608.02741
openalex publication_date 2016/08/09 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Several results regarding the stability and the stabilization of linear\nimpulsive positive systems under arbitrary, constant, minimum, maximum and\nrange dwell-time are obtained. The proposed stability conditions characterize\nthe pointwise decrease of a linear copositive Lyapunov function and are\nformulated in terms of finite-dimensional or semi-infinite linear programs. To\nbe applicable to uncertain systems and to control design, a lifting approach\nintroducing a clock-variable is then considered in order to make the conditions\naffine in the matrices of the system. The resulting stability and stabilization\nconditions are stated as infinite-dimensional linear programs for which three\nasymptotically exact computational methods are proposed and compared with each\nother on numerical examples. Similar results are then obtained for linear\npositive switched systems by exploiting the possibility of reformulating a\nswitched system as an impulsive system. Some existing stability conditions are\nretrieved and extended to stabilization using the proposed lifting approach.\nSeveral examples are finally given for illustration.\n