Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems

摘要

Several results regarding the stability and the stabilization of linearimpulsive positive systems under arbitrary, constant, minimum, maximum andrange dwell-time are obtained. The proposed stability conditions characterizethe pointwise decrease of a linear copositive Lyapunov function and areformulated in terms of finite-dimensional or semi-infinite linear programs. Tobe applicable to uncertain systems and to control design, a lifting approachintroducing a clock-variable is then considered in order to make the conditionsaffine in the matrices of the system. The resulting stability and stabilizationconditions are stated as infinite-dimensional linear programs for which threeasymptotically exact computational methods are proposed and compared with eachother on numerical examples. Similar results are then obtained for linearpositive switched systems by exploiting the possibility of reformulating aswitched system as an impulsive system. Some existing stability conditions areretrieved and extended to stabilization using the proposed lifting approach.Several examples are finally given for illustration.