In this paper, state estimation and adaptive sliding mode control (SMC) of uncertain fractional-order Markovian jump systems (FO-MJSs) with time delay and input nonlinearity are considered. A non-fragile observer is proposed to estimate the system states, and an observer-based adaptive sliding mode controller is synthesized to ensure the reachability of the sliding surfaces in the state-estimation space in finite time. The sufficient condition for stochastic stability of the error system and sliding mode dynamics is derived in the form of linear matrix inequalities (LMIs). Finally, some numerical examples are presented to illustrate the effectiveness of the proposed method.

In this paper the problem of non‐fragile adaptive sliding mode observer design is addressed for a class of nonlinear fractional‐order time‐delay systems with uncertainties, external disturbance, exogenous noise, and input nonlinearity. An H∞ observer‐based adaptive sliding mode control considering the non‐fragility of the observer is proposed for this system. The sufficient asymptotic stability conditions are derived in the form of linear matrix inequalities. It is proven that the sliding surface is reachable in finite time. An illustrative example is provided which corroborates the effectiveness of the theoretical results.

This article is concerned with exponential mean square stabilization of stochastic systems driven by fractional Brownian motion subject to state‐delay and uncertainties by sliding mode control. By applying the proposed method, the states of the system reach the sliding surface in finite time. Then, some sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the mean‐square exponential stability of the sliding motion. The LMI conditions for mean‐square exponential stability of the sliding mode dynamics are derived by constructing a novel Lyapunov functional. Finally, a simulation example is presented which corroborates the accuracy of the results.

This article proposes a new [Formula: see text] sliding mode control strategy for stabilizing controller design for fractional-order Markovian jump systems. The suggested approach is based on the diffusive representation of fractional-order Markovian jump systems which transforms the fractional-order system into an integer-order one. Using a new Lyapunov–Krasovskii functional, the problem of [Formula: see text] sliding mode control of uncertain fractional-order Markovian jump systems with exogenous noise is investigated. We propose a sliding surface and prove its reachability. Moreover, the linear matrix inequality conditions for stochastic stability of the resultant sliding motion with a given [Formula: see text] disturbance attenuation level are derived. Eventually, the theoretical results are verified through a simulation example.

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.