Robust H∞ control of uncertain linear impulsive stochastic systems

This paper develops robust stability theorems and robust H ∞ control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous-time stochastic dynamics and unstable/unstabilizable discrete-time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete-time dynamics, and the systems in which both the continuous-time stochastic dynamics and the discrete-time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell-time condition. Then, a linear matrix inequality-based approach to the design of a robust H∞ controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach.