Computing impulsive equilibrium sets with respect to target zone for linear impulsive systems

Abstract

Linear impulsive control systems are convenient to formulate a venue of real-lifeproblems, from diseases treatment to aerospace guidance. To take into account that the originis the only formal equilibrium of such systems while usual control objective consist in stabilizinga desired target region that exclude it, a dierent concept of equilibrium { which includesperiodic/orbital trajectories { has been dened. This work presents a new characterization ofthe equilibrium sets respecting this target region for linear impulsive systems. Based on theLucasz-Markov theorem a tractable and non conservative description is obtained. Furthermore,to assess this description, the constrained equilibrium set is explicitly used in the formulationof a model-based controller.