Stability Analysis of Linear Impulsive Systems using Lie-Algebraic Methods

In this paper, we continue the investigation of uniform exponential stability for linear impulsive systems. The analysis is based on a certain Lie algebra defined from the system description. Prior work has focused on solvable Lie algebras that reveal a triangularly coupled system structure that, in turn, is amenable to an explicit Lyapunov stability analysis. Here we show that in the general case, an impulsive system's Lie algebra still serves to reveal a triangularly coupled structure. Additional conditions are then derived that are sufficient for the existence of a quadratic Lyapunov function for each subsystem.