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In this article, a novel sliding mode control (SMC) approach is proposed for the control of a class of underactuated systems which are featured as in cascaded form with external disturbances. The asymptotic stability conditions on the error dynamical system are expressed in the form of linear matrix inequalities. The control objective is to construct a controller such that would force the state trajectories to approach the sliding surface with an exponential policy. The proposed SMC has a simple structure because it is derived from the associated first-order differential equation and is capable of handling system disturbances and nonlinearities. The effectiveness of the proposed control method is validated using intensive simulations.

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In this paper, an linear matrix inequalities (LMI)-based second-order fast terminal sliding mode control technique is investigated for the tracking problem of a class of non-linear uncertain systems with matched and mismatched uncertainties. Using the offered approach, a robust chattering-free control scheme is presented to prove the presence of the switching around the sliding surface in the finite time. Based on the Lyapunov stability theorem, the LMI conditions are presented to make the state errors into predictable bounds and the parameters of the controller are obtained in the form of LMI. The control structure is independent of the order of the model. Then, the proposed method is fairly simple and there is no difficulty in the use of this scheme. Simulations on the well-known Genesio's chaotic system and Chua's circuit system are employed to emphasize the success of the suggested scheme. The simulation results on the Genesio's system demonstrate that the offered technique leads to the superior improvement on the control effort and tracking performance.

This paper proposes a novel recursive terminal sliding mode structure for tracking control of third-order chained–form nonholonomic systems in the presence of the unknown external disturbances. Finite-time convergence of the disturbance approximation error is guaranteed using the designed disturbance observer. Under the proposed terminal sliding model tracking control technique, the finite-time convergence of the states of the closed-loop system is guaranteed via Lyapunov analysis. A new reaching control law is proposed to guarantee the existence of the sliding mode around the recursive TSM surface in a finite-time. Simulation results are illustrated on a benchmark example of third-order chained-form nonholonomic systems: a wheeled mobile robot. The results demonstrate that the proposed control technique achieves promising tracking performance for nonholonomic systems.

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