Control design for Itô stochastic interval type-2 models with time-varying delays

Abstract

Abstract This paper is concerned with stabilization problem for Ito stochastic interval type-2 (IT2) fuzzy systems with time-varying delays and unmatched premises. This problem is more complicated and challenging since it needs to deal with stochastic perturbations and time-varying delays as well as interval type-2 fuzzy basis functions simultaneously. A delay-dependent Lyapunov–Krasovskii functional (LKF) approach is proposed to analyse the underlying systems. By generalized Ito isometry, the reciprocally convex combination and time delay decomposition, a good estimate of the Lie derivative of the LKF can be established. A less conservative stochastic stability condition is thus established in terms of the estimate of the Lie derivative of the LKF. Finally, in light of the analysis result obtained, a state feedback controller is developed, and the effectiveness of the proposed approach is also illustrated by using a Monte Carlo simulation.