Finite-time stability of linear time-varying systems with jumps

This paper deals with the finite-time stability problem for continuous-time linear time-varying systems with finite jumps. This class of systems arises in many practical applications and includes, as particular cases, impulsive systems and sampled-data control systems. The paper provides a necessary and sufficient condition for finite-time stability, requiring a test on the state transition matrix of the system under consideration, and a sufficient condition involving two coupled differential–difference linear matrix inequalities. The sufficient condition turns out to be more efficient from the computational point of view. Some examples illustrate the effectiveness of the proposed approach.