In this paper, a new control method based on the Linear Matrix Inequality is used to control the speed of a hybrid stepper motor. The proposed method is proved based on the Lyapunov criterion. The proposed method has a higher degree of freedom than conventional robust controllers, which can be used to better control the system. The proposed method also exhibits high robustness against the uncertainty of the hybrid stepper motor parameters as well as the applied disturbances. Also in this method, the effect of rapid changes in the reference speed of the hybrid stepper motor are considered so that the controller can have more effective tracking. The proposed control method is compared with the Self-tuning PI controller and PI (Ziegler-Nichols) controller in multiple scenarios considering the uncertainty of the parameters and different disturbances. The obtained results indicate that the proposed controller has a better performance against the disturbances and uncertainty of the parameters in comparison with the abovementioned controllers. It should be noted that the simulations have been performed in Matlab.

With the presence of distributed energy resources in the microgrid, the problem of load-frequency control (LFC) becomes one of the most important concerns. With changing the parameters of the microgrid components as well as the disturbances forced to the grid, designing a suitable LFC becomes more difficult. In this paper, the design of a Robust model predictive controller (RMPC) based on the Linear Matrix Inequality as a secondary controller LFC system is discussed for controlling a microgrid on the shipboard. The main purpose of the proposed method is to improve the frequency stability of the microgrid in the presence of disturbances and the uncertainty of its parameters. The proposed controller simulation results, in several different scenarios, considering The uncertainty of the microgrid parameters as well as the input disturbances are compared. The main controllers are the fuzzy proportional-integral type1 and 2, and multi-objective multi-purpose functions optimized with the MOFPI (MBBHA), MOIT2FPI (MBHA) algorithm. The effectiveness of the proposed method in terms of The response speed and reduction of fluctuations and overcome uncertainties of the parameters, as well as robustness to disturbances, are discussed. Simulation is implemented in MATLAB software. The proposed method reduces the frequency oscillations caused by disturbances on the microgrid by 68% (68% improvement over other methods used in this field). Also, using this method, the damping speed of microgrid frequency fluctuations is increased by 53% (performance improvement).

In this paper, limitation in actuator capacity has been used as a key role in the design of the flight control system. In order to guarantee the performance and stability of flight control systems in the presence of saturation, in flying high angle of attack area, the development of Linear Matrix Inequality, optimization techniques, and numerical methods are proposed. Also, in this paper, the combination of two anti-windup methods and the direct saturation method in the tracking problem of the flight path angle is discussed. For this purpose, the nonLinear model of the aircraft is modeled, moreover the Linear model is obtained at the trim operation conditions. Then the controller is designed to track flight path angle maneuver regardless of saturation. In the following, considering the maximum disturbance involved in aircraft maneuvering, a safe controller that guarantees performance and stability is designed, and the gain scheduling technique to prevent conservatism in the use of controllers is applied. The results of the nonLinear and Linear model of the aircraft are presented in tracking flight path angle atahigh angle of attack with consideration of control and saturation constraints in unstable operation conditions. Simulation results indicate the improvement of the mentioned control method for an unstable aircraft.

This paper considers an optimal sliding mode control based on the cost control guaranteed approach using the Linear quadratic regulator method to stabilize delay fractional under involved disturbance. We propose an approach to an open research problem in the design of an LMI-based sliding mode controller in which there are some constraints such as optimizing system performance. The sliding mode technique is well-known as an effective tool for calculating the transient response of the system and achieving robust system performance. LQR classic techniques are less effective for studying an optimal fractional system in the presence of disturbance due to nonLinearity, so we use the optimal sliding mode approach control law designed for the nominal system and, then, combined it with a fractional sliding mode controller. By using the Razumikhin theorem for the stability of fractional order systems with delay and Linear Matrix Inequality, conditions on asymptotically stabilization were obtained . The presented controller stabilizes the nominal system and guarantees an adequate level of system performance. The sliding mode controller presented in the article, in addition to eliminating the effect of disturbance in the system, is independent of the delay A numerical example was provided to illustrate the effectiveness of the main results.

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The present study proposes a short-term memory discrete-time Finite Impulse Response (FIR) controller design along with an optimized tuning method. To this end, the loop shaping scheme was employed in the framework of Linear Matrix Inequalities (LMIs) to adjust some characteristics of the open-loop frequency response such as phase margin and bandwidth to the desired values at appropriate frequencies. Unlike the conventional methods whose functions are based on state-space models, the proposed procedure generates LMIs directly in the frequency domain. The proposed controller design procedure was applied to several integrating time-delay systems to illustrate its performance, and the obtained results were compared with the results of some other competing methods.

The classical Bohr Inequality says that |a+b|2 £ p½a½2+q½b½2 for all scalars a, b and p, q > 0 with 1/p + 1/q = 1. The equality holds if and only if (p-1)a = b. Several authors discussed operator version of Bohr Inequality. In this paper, we give a unified proof to operator generalizations of Bohr Inequality. One viewpoint of ours is a Matrix Inequality, and the other is a generalized parallelogram law for absolute value of operators, i.e., for operators A and B on a Hilbert space and t¹0, ½A-B½2+ 1/t½T A+B½2= (1+t) A½2 +(1+1/t) B½2.