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In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

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In order to extract efficient power generation, a wind turbine (WT) system requires an accurate maximum power point tracking (MPPT) technique. Therefore, a novel robust variable-step perturb-and-observe (RVS-P&O) algorithm was developed for the machine-side converter (MSC). The control strategy was applied on a WT based permanent-magnet synchronous generator (PMSG) to overcome the downsides of the currently published P&O MPPT methods. Particularly, two main points were involved. Firstly, a systematic step-size selection on the basis of power and speed measurement normalization was proposed; secondly, to obtain acceptable robustness for high and long wind-speed variations, a new correction to calculate the power variation was carried out. The grid-side converter (GSC) was controlled using a second-order sliding mode controller (SOSMC) with an adaptive-gain super-twisting algorithm (STA) to realize the high-quality seamless setting of power injected into the grid, a satisfactory power factor correction, a high harmonic performance of the AC source, and removal of the chatter effect compared to the traditional first-order sliding mode controller (FOSMC). Simulation results showed the superiority of the suggested RVS-P&O over the competing based P&O techniques. The RVS-P&O offered the WT an efficiency of 99.35%, which was an increase of 3.82% over the variable-step P&O algorithm. Indeed, the settling time was remarkably enhanced; it was 0.00794 s, which was better than for LS-P&O (0.0841 s), SS-P&O (0.1617 s), and VS-P&O (0.2224 s). Therefore, in terms of energy efficiency, as well as transient and steady-state response performances under various operating conditions, the RVS-P&O algorithm could be an accurate candidate for MPP online operation tracking.