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Brushless direct current motors have been considered by many researchers due to their many advantages over other direct current motors. The upper band is unknown and aims to converge in a limited time. For this purpose, by rewriting the motor model in the presence of modeling uncertainties and limited external perturbations, the terminal slip mode control law is designed to stabilize the system and converge the output speed and motor flow to the desired values ​​in a finite time, using the development theorem. In this control law, the high bandwidth of total uncertainties and external disturbances is estimated online using an adaptive law. Finally, while calculating the system convergence finite time, an idea to reduce the umbrella in using the terminal slip mode control is presented. The results of the numerical simulations performed show the accuracy of the designed controllers.

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Satellites attitude control based on their mission always is one of the main challenges in attitude control. Actually, in a certain class of satellites when satellites placed in a predetermined attitude or axis, sometimes an oscillating or chaotic behavior occurs, therefore, various models have been presented to analyze of this class. In this paper, H∞  Robust output feedback control under saturation is designed for this class of satellites that are also under external disturbance. The main point in this paper actually is design of the static output feedback (SOF) controller in the mentioned conditions in the form of solving a linear matrix inequality (LMI) problem. Then, in the same way, the stable region (B_∈) based on Lyapunov's theorem is obtained, which finally enlarges the region of attraction (ROA) for this control system. The proposed method was implemented on the presented model and the results showed that in addition to the appropriate speed of the system states in convergence, the control signal did not enter the saturation area and the system has become stable with the least cost and energy. The procedure design of output feedback controller is specified in the form of pseudo-code.