Paper presents a new method for implementing Oustaloup approximation of non-integer order systems in digital environment. Classical method and its limitations are presented and discussed. Method of realization is formulated and schemes for discretization are presented. Operation of method is illustrated with two examples. Work is ended with discussion of method limitations and conclusions.

Typical approach to non-integer order filtering consists of analogue design and implementation. Digital realization of non-integer order systems is susceptible to problems such as infinite memory requirement and sensitivity to numerical errors. The aim of this paper is to present two efficient methods for digital realization of non-integer order filters: discrete time-domain Oustaloup approximation and Laguerre impulse response approximation. Properties of both methods are investigated with use of non-integer low-pass filter. Filters realized with presented methods are then used for filtering of EEG signal. Paper concludes with discussion of merits and flaws of both methods.

Currently, there are no formalized methods for tuning non-integer order controllers. This is due to the fact that implementing these systems requires using an approximation of the non-integer order terms. The Oustaloup approximation method of the $s^{\alpha }$ fractional derivative is intuitive and widely adopted in the design of fractional-order PI${}^{\lambda }$D controllers. It requires special considerations for real-time implementations as it is prone to numerical instability. In this paper, for design and tuning of fractional regulators, we propose two methods.The first method relies on Nyquist stability criterion and stability margins. We base the second on parametric optimization via Simulated Annealing of multiple performance indicators. We illustrate our methods with a case study of the PI${}^{\lambda }$D controller for the Magnetic Levitation System. We illustrate our methods’ efficiency with both simulations and experimental verification in both nominal and disturbed operation.

Modern, based on biomedical signals interfaces have become recently very complex, however the complexity does not always lead to increased functionality or usability. In particular, when it comes to handicapped users, the currently available solutions are far from satisfactory. In this paper an innovative approach for biomedical signals based interfaced with the implementation of an inexpensive gaming headset Emotiv EPOC was presented. The main goal was to design, and develop an intuitive and user-friendly interface based on implementation of various biomedical signals such as EEG or EMG. The project was primarily intended for handicapped users as a replacement for traditional interfaces such as keyboard or mouse, however its potential use was extended. The proposed system differs from the already existing interfaces mainly because of its versatility to work with various biomedical signals, thus enabling a single interface to be controlled with different devices. Initial investigation has proven that Emotiv EPOC headset could be applied as an inexpensive, easily available on the open market tool for HumanComputer Interaction (HCI) systems for the gaming purpose.

Paper presents certain properties of Lyapunov direct method for non-integer order systems. Mittag-Leffler stability is defined and its relationship with Lyapunov stability is investigated. General results for Lyapunov functions are presented and a new result allowing constructive stability analysis is proved. Results are illustrated with the examples of stability analysis for problem of cooling, chemical reaction evolution and parametric stability analysis. DOI: http://dx.doi.org/10.5755/j01.eee.21.2.11505

Analysis of Electroencephalography (EEG) signals has recently awoken the increased interest of numerous researchers all around the world with regard to rapid development of Brain-Computer Interaction-related research areas and because EEG signals are implemented in most of the non-invasive BCI systems, as they provide necessary information regarding activity of the brain. In this paper, a very early stage pilot study on implementation of filtering based on fractional-order calculus (Bi-Fractional Filters – BFF) for the purpose of EEG signal classification is presented in brief.