Maglev vehicles have become a new type of transportation system with higher speed, lower noise, and commercial appeal. Magnetic-suspension systems, which have high nonlinearity and open-loop instability, are the core components of maglev vehicles. The high-performance control of maglev vehicles has been the focus of numerous studies. Encountering challenges in the levitation control of maglev vehicles in the form of uncertain time delays and disturbances is unavoidable. To cope with these problems, this study presents the design of an adaptive robust controller based on the Riccati method and sliding-mode technology, simultaneously taking into account the influence of time delays and disturbances. The asymptotic stability of the closed-loop system with the proposed control law is proved by the Lyapunov method. Control performances of the proposed controller are shown in the simulation results. Together with the consistently stabilizing outputs, the presented control approach can handle time delays and disturbances well. Finally, experiments were also implemented to examine its practical control performance of the robust levitation-control law.high-speed maglev train, as the world's first high-speed commercial maglev line, has been successfully open to traffic since December 2002, with a maximum operating speed of 431 km/h. In May 2016, the Changsha maglev line was put into trial operation and it reached the international leading level. In December 2017, Beijing's first medium-and low-speed maglev train, S1, began operations. A number of other cities and regions are also planning to introduce maglev technology. The official opening of the commercial operation line has met the basic requirements of engineering application, but there are still many technical difficulties, especially for the analysis and design of a levitation-control system.During complex working conditions and long-term passenger service, some problems occur in the levitation system that do not occur in laboratories or the short-term test-line assessments. These emerging problems seriously affect the stability and reliability of the levitation system and even cause the partial suspension-point failure of the vehicle, which affects the comfort and riding experience of the maglev train, and even hinders the application of more commercial maglev-transportation systems. These problems are closely related to the performance of the levitation-control system. In the past few decades, studies on magnetic-suspension systems have received much interest. Yan J D [6] utilized a Back Propagation (BP) neural network to adjust online parameters with a PI (proportional -integral) controller according to electromagnetic suspension acceleration and operation speed, and simulation results showed the effective suppression of electromagnetic vibration and the improvement of vehicle riding comfort. Sun [7] proposed an adaptive neural-fuzzy controller with sliding-mode technology that could achieve excellent dynamic performance under disturbance and uncertainty. He et al...

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