A non-fragile robust observer design for uncertain time-delay fractional Itô stochastic systems with input nonlinearity: An SMC approach

Abstract

This article considers the problem of non-fragile observer design for uncertain fractional Itô stochastic systems. The design is based on a sliding surface whose reachability in finite time is guaranteed by introducing a novel sliding mode control law. Employing the fractional infinitesimal operator and the related lemmas, the stochastic stability of the overall closed-loop system is transformed to the problem of solving a set of linear matrix inequalities. Addressing the fragility issue, a norm-bounded term is added to the observer gain, which prevents failure of the estimation error system. The adverse effects of the input nonlinearity and time-varying delay are alleviated by the proposed approach. Furthermore, the present method is investigated for the fractional Itô stochastic systems with known states. A numerical example is presented to illustrate the effectiveness of the proposed method.