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This paper presents a methodological approach to design observer-based adaptive sliding mode control for a class of nonlinear uncertain state-delayed systems with immeasurable states. A novel switching surface is proposed and a state observer is employed to reconstruct the sliding mode control action. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation technique so that the reaching condition can be satisfied. Based on Lyapunov stability theorem and linear matrix inequality (LMI) technique, the stability of the overall closed-loop nonlinear uncertain state-delayed system is guaranteed for the proposed control scheme under certain conditions. Furthermore, the state observer and control law can be constructed from the positive-definite solutions of two LMIs, and the design technique is simple and efficient. The validity of the proposed control methodology is demonstrated by simulation results.

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A discrete-time integral sliding mode control scheme is proposed to realize the problem of robust tracking and modeling following for a class of uncertain linear systems. It will be shown that the proposed scheme guarantees the stability of closed-loop system and achieves zero-tracking error in the presence of parameter uncertainties and external disturbances. The selection of switching surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against system uncertainties and disturbances. Chattering phenomenon and reaching phase are eliminated. Moreover, the knowledge of upper bound of uncertainties is not required. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme.

This paper investigates the synchronization problem for a class of uncertain chaotic systems. Only partial information of the system states is known. An adaptive sliding mode observer-based slave system is designed to synchronize a given chaotic master system with unknown parameters and external disturbances. Based on the Lyapunov stability theorem, the global synchronization between the master and slave systems is ensured. Furthermore, the structure of the slave system is simple and the proposed adaptive sliding mode observer-based synchronization scheme can be implemented without requiring a priori knowledge of upper bounds on the norm of the uncertainties and external disturbances. Simulation results demonstrate the effectiveness and robustness of the proposed scheme.

A new discrete‐time adaptive global sliding mode control (SMC) scheme combined with a state observer is proposed for the robust stabilization of uncertain nonlinear systems with mismatched time delays and input nonlinearity. A state observer is developed to estimate the unmeasured system states. By using Lyapunov stability theorem and linear matrix inequality (LMI), the condition for the existence of quasi‐sliding mode is derived and the stability of the overall closed‐loop system is guaranteed. Finally, simulation results are presented to demonstrate the validity of the proposed scheme.