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Diagnosis of discrete-time singularly perturbed systems based on slow subsystem

Tellili A., Abdelkrim N., Jaouadi B., Abdelkrim M. N.

Acta Mechanica et Automatica

2014

Vol. 8, no. 4

175--180

This paper deals with the diagnosis of discrete-time singularly perturbed systems presenting two time scales property. Parity space method is considered to generate the fault detection residual. The focus is in two directions. First, we discuss the residual illconditioning caused by the singular perturbation parameter. Then, the use of the slow subsystem is considered to make the fault diagnosis easier. It is shown that the designed diagnostic algorithm based on reduced order model is close to the one synthesized using the full order system. The developed approach aims at reducing the computational load and the ill-conditioning for stiff residual generation problem. Two examples of application are used to demonstrate the efficiency of the proposed method.

Maximal stability bounds of discrete-time singularly perturbed systems

Chen S.-J, Lin J.-L.

Control and Cybernetics

2004

Vol. 33, no. 1

95-108

The exact stability bound of the parasitic parameter for a discrete-time singularly perturbed system is determined by the linear fractional transformation (LFT) framework. Two systematic approaches including time-domain and frequency-domain methods are proposed to solve this problem based on the unified LFT framework. One employs the Kronecker product of LFTs and the guardian map theory. The other is to plot the eigenvalue loci of a real rational function matrix. Two examples are given to show the feasibility of the approaches.