Abstract : Linear impulsive control systems are convenient to formulate a venue of real-life problems, from diseases treatment to aerospace guidance. To take into account that the origin is the only formal equilibrium of such systems while usual control objective consist in stabilizing a desired target region that exclude it, a different concept of equilibrium-which includes periodic/orbital trajectories-has been defined. This work presents a new characterization of the equilibrium sets respecting this target region for linear impulsive systems. Based on the Lucasz-Markov theorem a tractable and non conservative description is obtained. Furthermore, to assess this description, the constrained equilibrium set is explicitly used in the formulation of a model-based controller.
Christophe Louembet, Alejandro Hernan Gonzalez, Ignacio Sanchez. Computing impulsive equilibrium sets with respect to target zone for linear impulsive systems. 21st IFAC World Congress, Jul 2020, Berlin, Germany. ⟨hal-02403599⟩