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This paper studies the sliding mode control method for coupled delayed fractional reaction-diffusion Cohen–Grossberg neural networks on a directed non-strongly connected topology. A novel fractional integral sliding mode surface and the corresponding control law are designed to realize global Mittag-Leffler synchronization. The sufficient conditions for synchronization and reachability of the sliding mode surface are derived via the hierarchical method and the Lyapunov method. Finally, simulations are provided to verify our theoretical findings. [ABSTRACT FROM AUTHOR]

The current work has proposed an approach to the controller design of a fuzzy non-singular terminal sliding mode (NTSM) for a type of planar systems with input saturation. On the basis of a modified version of NTSM, a category of saturated NTSM controller is first constructed to ensure that the states can reach the sliding surface and finite-time converge to the origin. On this basis, a fuzzy logic controller including two fuzzy input variables and a fuzzy output variable is developed to adaptively adjust the control gain such that the gain of the NTSM controller can be automatically minimized. This also implies that the chattering phenomenon encountered by most conventional sliding mode control (SMC) schemes can be significantly attenuated without sacrificing inherent properties. Finally, in comparison with a traditional SMC method, the superiority of the presented algorithm is confirmed by the comparative simulation results in terms of chattering alleviation and robustness. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of robust H∞ sliding mode control for a class of singular stochastic nonlinear systems. Integral sliding mode control is developed to deal with this problem. Based on the integral sliding surface of the design and linear matrix inequality, a sufficient condition which guarantees the sliding mode dynamics is asymptotically mean square admissible and has a prescribed H∞ performance for a class of singular stochastic nonlinear systems is proposed. Furthermore, a sliding mode control law is synthesized such that the singular stochastic nonlinear system can be driven to the sliding surface in finite time. Finally, a numerical example is proposed to illustrate the effectiveness of the given theoretical results. [ABSTRACT FROM AUTHOR]

This paper mainly investigates two kinds of sliding mode synchronization (SMS) for multiple chaotic systems with unknown parameters and disturbances. Both multiple coupled systems and uncoupled systems are considered. For multiple uncoupled chaotic systems (MUCSs), the sliding mode control scheme is designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances, and the appropriate adaptive laws are proposed to estimate unknown parameters. For multiple coupled chaotic systems (MCCSs), the definition of transmission synchronization is given first. Furthermore, a special integral sliding surfaces is selected, and the corresponding controllers with the compensation terms are developed to realize SMS between every drive chaotic system and every respond system in transmission mode. Finally, some numerical examples are presented to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates two classes of synchronization problems of multiple chaotic systems with unknown uncertainties and disturbances by employing sliding mode control. Modified projective synchronization and transmission synchronization are discussed here. For the modified projective synchronization problem, sliding mode controllers are designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances. For the transmission synchronization problem, based on adaptive sliding mode control, an integral sliding surface is selected and the adaptive laws are derived to tackle unknown uncertainties and disturbances for such systems. A class of nonlinear adaptive sliding mode controllers is developed to guarantee asymptotical stability of the error systems so that all chaotic systems can synchronize with each other. Simulation results are given to illustrate the effectiveness of the proposed schemes by comparing with the existing methods. [ABSTRACT FROM AUTHOR]

• As a first attempt, the SMC problem of PDT switched nonlinear systems is addressed, and the dynamic ET mechanism is introduced to alleviate the limited bandwidth resources, which is more general. • With the dynamic ET mechanism, a new switched SMC law is constructed with the PDT switching strategy that is more general than DT and ADT switching strategies, which can match the subsystem one by one more reasonably and reduce the conservativeness to some extent. • Based on the Lyapunov function approach, some sufficient conditions, which can ensure both the reachability and globally uniform exponential stability with an H ∞ performance of the closed-loop PDT switched system, are derived. In this paper, the H ∞ sliding mode control problem of persistent dwell-time switched nonlinear systems is investigated. Due to the limited bandwidth resources, a dynamic event-triggered mechanism is introduced to alleviate the transmission burden. Considering that the system parameters are switched in accordance with the persistent dwell-time switching strategy, a novel switched sliding mode control law is constructed. Then, drawing on the Lyapunov function approach, sufficient conditions are derived, which not only ensure the reachability of the sliding region around the specified sliding surface but also guarantee the globally uniform exponential stability of the system with an H ∞ performance. Moreover, the specific form of the controller gains is derived by utilizing an efficient decoupling method. Eventually, the validity of the proposed method is validated by two numerical examples. [ABSTRACT FROM AUTHOR]

• As the first attempt, we considered the state information required by the sliding mode controller will be randomly dropouts, which is reflected in the obtained equivalent sliding mode controller. • A novel method is utilized for the SMC problem of the PDT switched systems with data dropouts, and a novel SMC law is proposed. • For the PDT switched systems, some sufficient conditions to guarantee the mean-square exponential stability with data dropouts are derived for the PDT switched systems and the H ∞ performance of the system is analyzed through utilizing the linear matrix inequality technique. This paper concentrates on the sliding mode control problem for a set of discrete-time switched systems. As the first attempt, the persistent dwell-time switching rule is considered in the research of sliding mode control for switched systems. Furthermore, data dropouts are frequently encountered in the process of data transmission, and it should be considered in the process of designing the sliding mode control law so that the state trajectories are guaranteed to move in a region around the specified sliding surface. Based on the Lyapunov theory and the matrix convex optimization technique, the main concern of this paper is to construct a sliding mode controller to ensure that the closed-loop system is mean-square exponentially stable with a prescribed weighted H ∞ performance. Finally, the effectiveness and rationality of the obtained results are verified by a numerical example. [ABSTRACT FROM AUTHOR]

• Compared with the previous works about MJSPSs that the controller was assumed to directly obtain the system mode, we utilize the HMM to describe this asynchronous phenomenon, thus the designed controller is more general and appropriate. • Aiming at the Markov jump and singularly perturbed parameter (SPP) in the system, a proper mode-independent sliding surface and an asynchronous SMC law in consideration of the singularly perturbed parameter matrix are proposed based on the HMM approach. • As the first attempt, the fault-tolerant control scheme is applied in the asynchronous SMC for MJSPSs. Combined with it, the mean-square stability with an acceptable H ∞ system performance is achieved. This work studies the asynchronous fault-tolerant sliding mode control for uncertain stochastic jumping systems subject to singular perturbations, in which the controller is assumed to be able to estimate the hidden system mode through a detector with a conditional probability via the hidden-Markov model. Additionally, in consideration of avoiding the system performance decreases generated by the actuator degradation, the synthesized fault-tolerant sliding mode control scheme is first employed. Through applying a common singularly perturbed parameter based sliding surface, this paper attempts to construct a proper asynchronous sliding mode control law that can ensure not only the reachability but also the closed-loop system is stable with an expected H ∞ performance index. By virtue of the mode-dependent Lyapunov function and the hidden-Markov model approach, sufficient conditions are acquired. Besides, solving linear matrix inequalities for obtaining the control gain matrices are given through the convex optimization theory. Eventually, the effectiveness and feasibility of the proposed asynchronous fault-tolerant sliding mode control scheme are verified by a numerical example. [ABSTRACT FROM AUTHOR]