Lie-algebraic conditions for stability of linear impulsive systems

This paper presents Lie-algebraic conditions for a type of exponential stability for linear impulsive systems that is uniform with respect to the set of impulse times. A Lie algebra is defined in terms the linear impulsive system data to which previously-derived Lie-algebraic stability criteria for switched linear systems are applied in order to yield sufficient conditions for uniform exponential stability of linear impulsive systems. An example is presented to illustrate the main ideas and some of the underlying computational aspects.