In this paper, a systematic design procedure for generalized projective synchronization between two identical chaotic satellites systems based on feedback control theory is proposed. This method is developed based on suitable feedback control, combined with the Lyapunov stability theory and linear matrix inequality formulation as a solution of the optimal problem. Two necessary and sufficient conditions for the asymptotic stability of the error dynamic system are obtained. Compared with the predictive-based control method, the proposed method shows comparable and superior performance. The effectiveness of the obtained results is illustrated by numerical simulations.

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This paper addresses asymptotic stabilization of uncertain nonlinear fractional-order systems with bounded inputs in the presence of model uncertainties and external disturbances. To develop the idea, it is assumed that the upper bound of perturbations is a nonlinear function of the pseudostates norm in which its coefficients are unknown and are obtained via proposed adaptive laws. The main contribution of this paper is to develop a new bounded fractional-order chattering free adaptive sliding mode control in which the system states converge to the sliding surface at a predefined finite time. The stability of the closed-loop system with the proposed control scheme is guaranteed by the Lyapunov theory. Furthermore, for more clarification, a comparison with the classical integer-order case is also presented; finally, some practical simulation results are provided to show the effectiveness of the proposed control algorithm.

In this paper, an approach for optimal tuning of fractional order proportional derivative (FOPD) and a certain class of fractional order proportional integral derivative (FO-PID) controllers for integer-order integrating time delay systems based on frequency method is developed. For this purpose, particle swarm optimization (PSO) algorithm has been used for optimal controller parameters tuning. Performance of the proposed tuning method obtained by using these PD and PID controllers with PSO algorithm with the results without using PSO is compared. The investigations revealed that the proposed algorithm is relatively simple, reliable and efficient and suitable for controlling integer-order integrating time delay systems.Key words: Fractional order proportional derivative (FOPD), fractional order proportional integral derivative (FO-PID), Integrating time delay system, particle swarm optimization, stability boundary locus.