Measurable disturbance decoupling for hybrid linear systems with periodic state jumps

This paper is focused on hybrid linear systems subject to periodic state jumps. The measurable disturbance decoupling problem investigated is a synthesis problem with a twofold objective: rendering the system output insensitive to a disturbance accessible for measurement and, at the same time, achieving global asymptotic stability of the compensated hybrid linear dynamics for the jump time sequence with the given period. In order to best exploit the real-time knowledge of the disturbance, a feedforward compensation scheme is adopted, under the assumption that the plant is prestabilized by a suitable feedback. Hence, a necessary and sufficient solvability condition is proven. Such condition is constructive: i.e., the proof outlines the procedure for deriving a hybrid linear feedforward compensator that satisfies the stated requirements.