Adaptive sliding-mode-based control for stochastic nonlinear systems subject to probabilistic interval delay: A delay-fractioning method

Abstract

This paper is concerned with the design problem of adaptive sliding mode control (SMC) scheme for uncertain continuous stochastic nonlinear systems subject to probabilistic interval delay. The probabilistic interval delay is considered and a Bernoulli distributed stochastic variable with known conditional probability is utilized to characterize the delay characteristic. By introducing new Lyapunov–Krasovskii functional, some sufficient criteria via the delay-fractioning idea are obtained to discuss the stochastic stability of the resultant sliding motion, which are represented by some linear matrix inequalities (LMIs) satisfying certain constraint. Subsequently, the solvability of non-convex problem is testified by the feasibility of a minimization one and a computational algorithm is provided. Besides, an adaptive SMC method is given to ensure the reachability criterion of designed integral-type sliding surface. Finally, the validity of newly proposed SMC strategy based on adaptive mechanism is illustrated by some simulations.