Finite-time stabilization of impulsive dynamical linear systems

This paper deals with the finite-time stability problem for a special class of hybrid systems, namely impulsive dynamical linear systems (IDLS). IDLS are systems that exhibit jumps in the state trajectory. Both analysis and design problems are tackled, both for time-dependent and state-dependent IDLS. The presented results require to solve feasibility problems involving Differential Linear Matrix Inequalities (DLMIs), which can be solved numerically in an efficient way, as illustrated by the proposed example.