Stability of interconnected impulsive switched systems subject to state dimension variation

The contribution of this article is twofold. First we deal with the stability of continuous-time interconnected impulsive switched systems for which the dimension of the system’s state vector may change at different modes. A dwell time condition is derived to ensure the exponential convergence of the state trajectories, and when the system is subject to a non-vanishing perturbation, a superior bound of the state trajectories is provided as well. The main advantage of the solution we propose is its direct application to practical fields such as metallurgy or traffic control through the use of semi-definite programming solvers. Second, we introduce in the framework a platoon of vehicles in automated highway systems where vehicles may join or leave the platoon. Then, we detail the longitudinal stability problem of such a system and illustrate the features of the proposed stability conditions through numerical simulations.