Displaying similar documents to “Fractional hold circuits versus positive realness of discrete transfer functions.”

Normalized finite fractional differences: Computational and accuracy breakthroughs

Rafał Stanisławski, Krzysztof J. Latawiec (2012)

International Journal of Applied Mathematics and Computer Science

Similarity:

This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated...

Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

Tadeusz Kaczorek (2013)

International Journal of Applied Mathematics and Computer Science

Similarity:

Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.

Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains

Piotr Ostalczyk (2012)

International Journal of Applied Mathematics and Computer Science

Similarity:

Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.

Robust fractional adaptive control based on the strictly Positive Realness Condition

Samir Ladaci, Abdelfatah Charef, Jean Jacques Loiseau (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed...

Design of unknown input fractional-order observers for fractional-order systems

Ibrahima N'Doye, Mohamed Darouach, Holger Voos, Michel Zasadzinski (2013)

International Journal of Applied Mathematics and Computer Science

Similarity:

This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach,...