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In this note some points to paper [L. Pan, W. Zhou, J. Fang, D. Li, Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control, Commun Nonlinear Sci Numer Simulat 2010;15:3754-3762] are presented. Hereby, we illustrate that the way that authors in [1] treat with fractional version of Lyapunov stability theorem suffers lack of a correct justification  

In this paper, the swing-up problem of the Furuta pendulum has been solved by introducing a new combined method based on the frequency response, and the sliding mode method. Furthermore, a trajectory tracking controller has been introduced and applied to the Furuta pendulum; which the pendulum remained regulated at the upward position, while the arm tracks a desired time-varying trajectory. The hierarchical sliding mode control (HSMC) approach has been employed to achieve the mentioned goals. The Furuta system is made up of two subsystems. Based on this physical structure, the hierarchical structure of the sliding surfaces is designed as follows: first, the sliding surface of each subsystem... 

The main contribution of this paper is to introduce a novel non-Lipschitz protocol that guarantees consensus in finite-time domain. Its convergence in networks with both unidirectional and bidirectional links is investigated via Lyapunov Theorem approach. It is also proved that final agreement value is equal to average of agents' states for the bidirectional communication case. In addition effects of communication time-delay on stability are assessed and two other continuous Lipschitz protocols are also analyzed  

A new robust adaptive controller is developed for the control of the hepatitis B virus (HBV) infection inside the body. The non-linear HBV model has three state variables: uninfected cells, infected cells and free viruses. A control law is designed for the antiviral therapy such that the volume of infected cells and the volume of free viruses are decreased to their desired values which are zero. One control input represents the efficiency of drug therapy in inhibiting viral production and the other control input represents the efficiency of drug therapy in blocking new infection. The proposed controller ensures the stability and robust performance in the presence of parametric and... 

The problem of asymptotic stability analysis of equilibrium points in nonlinear distributed-order dynamic systems with non-negative weight functions is considered in this paper. The Lyapunov direct method is extended to be used for this stability analysis. To this end, at first, a discretisation scheme with convergence property is introduced for distributed-order dynamic systems. Then, on the basis of this tool, Lyapunov theorems are proved for asymptotic stability analysis of equilibrium points in distributed-order systems. As the order weight function assumed for the distributed-order systems is general enough, the results are applicable to a wide range of nonlinear distributed-order... 

This paper proposes a new design of robust control combining feedback linearization, backstepping, and sliding mode control called FLBS applied to the locomotion of five-link biped robot. Due to the underactuated robot's model, the system has a hybrid nature, while the FLBS control can provide a stabilized walking movement even with the existence of large disturbances and uncertainties by implementing smooth chatter-free signals. Stability of the method is proven using the Lyapunov theorem based on the hybrid zero dynamics and Poincaré map. The simulations show the controller performance such as robustness and chatter-free response in the presence of uncertainty and disturbance. © 2020... 

This paper proposes a new design of robust control combining feedback linearization, backstepping, and sliding mode control called FLBS applied to the locomotion of five-link biped robot. Due to the underactuated robot's model, the system has a hybrid nature, while the FLBS control can provide a stabilized walking movement even with the existence of large disturbances and uncertainties by implementing smooth chatter-free signals. Stability of the method is proven using the Lyapunov theorem based on the hybrid zero dynamics and Poincaré map. The simulations show the controller performance such as robustness and chatter-free response in the presence of uncertainty and disturbance. © 2020... 

This paper proposes a new design of robust control combining feedback linearization, backstepping, and sliding mode control called FLBS applied to the locomotion of five-link biped robot. Due to the underactuated robot's model, the system has a hybrid nature, while the FLBS control can provide a stabilized walking movement even with the existence of large disturbances and uncertainties by implementing smooth chatter-free signals. Stability of the method is proven using the Lyapunov theorem based on the hybrid zero dynamics and Poincaré map. The simulations show the controller performance such as robustness and chatter-free response in the presence of uncertainty and disturbance. Copyright ©... 

In this paper, the parameters of a 4D Lü hyper-chaotic system are identified via synchronization of two identical systems. Unknown parameters of the drive system are identified by an adaptive method. Stability of the closed-loop system with one state feedback controller is studied by using the Lyapunov theorem. Also the convergence of the parameters to their true values is proved. Then a fractional adaptation law is applied to reduce the time of parameter convergence. Finally the results of both integer and fractional methods are compared  

This paper describes a novel Direct Torque Control (DTC) method for adjustable speed Doubly-Fed Induction Machine (DFIM) drives which is supplied by a two-level Space Vector Modulation (SVM) voltage source inverter (DTC-SVM) in the rotor circuit. The inverter reference voltage vector is obtained by using input-output feedback linearization control and a DFIM model in the stator a-b axes reference frame with stator currents and rotor fluxes as state variables. Moreover, to make this nonlinear controller stable and robust to most varying electrical parameter uncertainties, a two layer recurrent Artificial Neural Network (ANN) is used to estimate a certain function which shows the machine...