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Nontrivial solutions of linear functional equations: methods and examples

Varga A., Vincze C.

Opuscula Mathematica

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2015

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Vol. 35, no. 6

957-972

EN

For a wide class of linear functional equations the solutions are generalized polynomials. The existence of non-trivial monomial terms of the solution strongly depends on the algebraic properties of some related families of parameters. As a continuation of the previous work [A. Varga, Cs. Vincze, G. Kiss, Algebraic methods for the solution of linear functional equations, Acta Math. Hungar.] we are going to present constructive algebraic methods of the solution in some special cases. Explicit examples will be also given.

2

Detection and identification of loss of efficiency faults of flight actuators

Ossmann D., Varga A.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

53--63

EN

We propose linear parameter-varying (LPV) model-based approaches to the synthesis of robust fault detection and diagnosis (FDD) systems for loss of efficiency (LOE) faults of flight actuators. The proposed methods are applicable to several types of parametric (or multiplicative) LOE faults such as actuator disconnection, surface damage, actuator power loss or stall loads. For the detection of these parametric faults, advanced LPV-model detection techniques are proposed, which implicitly provide fault identification information. Fast detection of intermittent stall loads (seen as nuisances, rather than faults) is important in enhancing the performance of various fault detection schemes dealing with large input signals. For this case, a dedicated fast identification algorithm is devised. The developed FDD systems are tested on a nonlinear actuator model which is implemented in a full nonlinear aircraft simulation model. This enables the validation of the FDD system’s detection and identification characteristics under realistic conditions.

3

Computing Generalized Inverse Systems Using Matrix Pencil Methods

Varga A.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no. 5

1055-1068

EN

We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil to appropriate Kronecker-like forms.