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Based on energy variation methods we calculated the deflection of membranes under the combined load of an external pressure and an internal lateral stress. A lateral load gives rise to buckling once a critical load is exceeded. The combination of transversal loads and lateral loads changes the properties of the membrane (and other structures) in the vicinity of the buckling load: The membrane deflects at all lateral loads and the critic load, above which two states are possible shifts. A result important for the design of microsystems, which are based on the buckling phenomenon, is the pressure required to switch the membrane from one state to the other. The theory is tested successfully with micromachined silicon/silicon-dioxide membranes.

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This paper investigates Lyapunov approaches to expand the domain of attraction (DA) of nonlinear autonomous models. These techniques had been examined for creating generic numerical procedures centred on the search of rational and quadratic Lyapunov functions. The outcomes are derived from all investigated methods: the method of estimation via Threshold Accepted Algorithm (TAA), the method of estimation via a Zubov technique and the method of estimation via a linear matrix inequality (LMI) optimization and genetic algorithms (GA). These methods are effective for a large group of nonlinear models, they have a significant ability of improvement of the attraction domain area and they are distinguished by an apparent propriety of direct application for compact and nonlinear models of high degree. The validity and the effectiveness of the examined techniques are established based on a simulation case analysis. The effectiveness of the presented methods is evaluated and discussed through the study of the renowned Van der Pol model.

The new FDerivatives code was conceived and developed for calculating static and dynamic stability derivatives of an aircraft in the subsonic regime, based on its geometrical data. The code is robust and it uses geometries and flight conditions to calculate the aircraft’s stability derivatives. FDerivatives contains new algorithms and methods that have been added to DATCOM’s classical method, presented in a USAF Stability and Control DATCOM reference. The new code was written using MATLAB and has a complex structure which contains a graphical interface to facilitate the work of potential users. Results obtained with the new code were evaluated and validated with flight test data provided by CAE Inc. for the Hawker 800XP business aircraft.

Extracting maximum energy from photovoltaic (PV) systems at varying conditions is crucial. It represents a problem that is being addressed by researchers who are using several techniques to obtain optimal outcomes in real-life scenarios. Among the many techniques, Maximum Power Point Tracking (MPPT) is one category that is not extensively researched upon. MPPT uses mathematical models to achieve gradient optimisation in the context of PV panels. This study proposes an enhanced maximisation problem based on gradient optimisation techniques to achieve better performance. In the context of MPPT in photovoltaic panels, an equality restriction applies, which is solved by employing the Dual Lagrangian expression. Considering this dual problem and its mathematical form, the Nesterov Accelerated Gradient (NAG) framework is used. Additionally, since it is challenging to ascertain the step size, its approximate value is taken using the Adadelta approach. A basic MPPT framework, along with a DC-to-DC convertor, was simulated to validate the results.

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