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Stability bound of discrete multiple time-delay singularly perturbed systems. (English) Zbl 1148.39003
The paper is concerned with the exact stability bound (with respect to a small parameter) for discrete multiple time-delay singularly perturbed systems. The main results are Theorems 1-3. First, the author proves a relation between the stability of the singularly perturbed system, the reduced slow and the fast subsystems for sufficiently small parameter. Then, by transforming the systems into auxiliary first order discrete-time systems (without time-delay) and applying a necessary and sufficicient condition for the stability of a matrix E. I. Jury and S. Gutman [IEEE Trans. Autom. Control 20, 533–535 (1975; Zbl 0308.15009)], exact stability bounds are obtained for both the singularly perturbed system and the fast subsystem. Finally, a concrete examle is given for illustrating the procedure of finding the stability bounds.

MSC:
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
34K20 Stability theory of functional-differential equations
34E15 Singular perturbations, general theory for ordinary differential equations
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