Robust H∞ control of switched stochastic systems with time delays under asynchronous switching

This paper investigates the problem of robust H∞ control for a class of switched stochastic systems with time delays under asynchronous switching, where the asynchronous switching means that the switching of the controllers has a lag to the switching of system modes. The parameter uncertainties are allowed to be norm bounded. Firstly, by using the average dwell time approach, the stability criterion and H∞ performance analysis for the underlying systems are developed. Then, based on the obtained results, sufficient conditions for the existence of admissible asynchronous switching controllers which guarantee that the resulting closed-loop systems are mean-square exponentially stable with H∞ performance are derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.