Aperiodic sampled-data robust [formula omitted] control for delayed stochastic fuzzy systems with quasi-periodical multi-rate approach

Abstract

This paper considers the robust H∞ problem of delayed stochastic T–S fuzzy systems with aperiodic sampled-data. In order to represent the sawtooth structure of sampled-data more vividly, we reconstruct the continuous time-varying delayed stochastic T–S fuzzy model with discrete feedback as an impulsive control model. Then, the quasi-periodical time-varying Lyapunov function method is introduced to cope with the mean-squared exponential stability of the multi-rate aperiodic sampling control problem and its H∞ performance. Otherwise, for the sake of determining the exact matrices Pm and Pm+1 of delayed matrix function P(t−d(t)), we design a new algorithm. Next, two theorems with the information of maximum and minimum sampling length and the size of time-delay are proposed to realize the H∞ performance. Since the single-rate controllers are the special case of the multi-rates’, the obtained results are less conservative than previous ones. Finally, a numerical example is given to illustrate our results.