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).

This paper is concerned with the problem of delay-dependent passive analysis and control for interval stochastic time-delay systems. The system matrices are assumed to be uncertain within given intervals, the time delay is a time-varying continuous function belonging to a given range, and the stochastic perturbation is in the form of a Brownian motion. By using ItO's differential formula and the Lyapunov stability theory, delay-dependent stochastic passive control criteria are proposed without ignoring any useful terms by considering the information of the lower bound and upper bound for the time delay. Based on the criteria obtained, a delay-dependent passive controller that ensures the stochastic passivity of the closed-loop system is presented. Then, the controller gain is characterized in terms of (LMI)s, which can be easily checked by resorting to available software packages. Numerical examples are given to demonstrate the effectiveness of the method.

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.

This paper deals with the study of asymptotic stability of zero solution of a kind of delay singular system. Based on the delayed-decomposition approach, two new results are obtained on the asymp-totic stability of the considered system by using some inequalities and Lyapunov-Krasovskii functionals (LKFs). Two examples with their numerical simulations are provided to illustrate effectiveness of the pro-posed method by MATLAB software.

The problem of robust nonfragile H∞filtering for fuzzy fractional order (FFO) systems 0 < α < 1 with uncertainties is studied. First, a new sufficient condition of H∞ control for fractional order systems is given to overcome the shortcoming of solving the complex Matrix. Then, based on the condition and the Linear Matrix Inequality ((LMI)) approach, the conditions of robust H∞ control for FFO systems are proposed, which can guarantee the prescribed noise attenuation level in the H∞ sense. Furthermore, the FFO filter is constructed, and sufficient conditions are proposed for FFO filter systems. Finally, two examples are given to verify the effectiveness of our conditions.

In this paper, the spacecraft formation flying using virtual structure algorithm is studied. In spacecraft formation flying, several small spacecraft have been used instead of employing single one to achieve the same goal. In virtual structure method, the position and orientation of each spacecraft is measured with respect to position and attitude of virtual node in every moment. Two robust control methods are proposed to control formation. At first, the robust m synthesis control method is used to attenuate the influence of the sensor noises, environment disturbances and parametric uncertainties but it is done with heavy computations. The second method is in the standard form of optimization problem. It is composed of state feedback controller and Lyapanov stability theory. The Linear Matrix Inequality ((LMI)) controller computations are very efficient and the controller is robust against parametric uncertainties and most of the disturbances. The implementation of control methods on virtual node guarantees robust stability and performance. Concerning actuator constraints, simulation example is provided to show the effectiveness of the proposed control schemes to track the desired attitude and position trajectories despite system uncertainties.