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In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches.

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This paper proposes an adaptive integral-type terminal sliding mode tracking control approach based on the active disturbance rejection for uncertain nonlinear systems subject to input saturation and external disturbances. Its main objective is to achieve zero tracking error in the presence of external disturbances, parametric uncertainties and input saturation; ubiquitous problems in most practical engineering systems. The proposed approach combines the robustness and chattering-free dynamics of adaptive integraltype sliding mode control with the estimation properties of a nonlinear extended state observer. It also assumes the bounds of the input saturation to be unknown. The asymptotic stability of the closed-loop system in the presence of disturbances, uncertainties and input saturation is proven using the Lyapunov theorem. The effectiveness of the proposed approach is assessed using a flexible-link robotic manipulator. The obtained results confirmed the robustness and god tracking performance of the proposed approach. Robustness, chattering-free dynamics and good tracking performance albeit input saturation are among the main features INDEX TERMS Active disturbance rejection; nonlinear system; terminal sliding mode control; input saturation; flexible-link manipulator.

This manuscript proposes a robust fixed time terminal sliding mode prototype for trajectory tracking of the nonlinear dynamics of an under-actuated air cushion vehicle. Nonlinearity, external disturbances, internal uncertainties and unmodeled dynamics are the main difficulties that an amphibious vehicle is faced with in its maneuver. The main contribution of the proposed methodology is to overcome these problems based on both the guaranteed stability in sense of Lyapunov and the fixed time tracking error even if the initial values are changed. Robustness against uncertainties and disturbances, fixed time convergence of tracking error to zero are other merits of the proposed approach. The simulation results demonstrate the effectiveness and superiority of suggested scheme.