Abstract
This paper treats linear systems which include autonomous jumps of the state trajectories and investigates their basic properties. First, we derive a necessary and sufficient condition for the system to be well-posed in terms of an algebraic expression. Second, we give a condition that the system provides an invariant set, and show that a condition under which the origin is asymptotically stable in the invariant set can be reduced to LMIs. Finally, a numerical example is given to illustrate the effectiveness of the proposed analysis method.
