Well-posedness and Stability Analysis of Linear Systems with Autonomous Jumps of State Trajectories

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.