Stability and Stabilization of Data-driven Discrete-time Linear Impulsive Systems

This paper studies the problems of stability and stabilization for data-driven linear discrete-time impulsive systems (LDTISs). Firstly, open-loop and closed-loop data-based system representations of LDTISs are given by utilizing persistently exciting data. While the open-loop data-based system representation is an identification-like result, the closed-loop case bypasses the system identification, which can be used for directly data-driven control law design. Secondly, by utilizing time-dependent Lyapunov function technique, stability criteria for data-based closed-loop system are derived, and a data-driven state feedback controller are designed. Such criteria are independent of system matrices and can be formulated into a set of linear matrix inequalities plus a class of linear matrix equations, which can be solved efficiently by CVX toolbox. Finally, an example is presented to verify the efficiency of the established data-driven control law.