1. Full name: Ngo Thi Thanh Nga                                    2. Sex: Female

3. Date of birth: 10-10-1981                                            4. Place of birth: Phu Tho.

5. Admission decision number: 4982/QĐ-ĐHKHTN, Dated on 27 November 2013 by the Rector of VNU University of Science.

6. Changes in academic process: Decision 1033/QĐ-ĐHKHTN, Dated on 25 April 2017  by the Rector of VNU University of Science on Extending 12 months.

7. Official thesis title: Stability and robust stability of singular linear difference equations.

8. Major: Differential and Integral Equation                       9. Code: 62 460103

10. Supervisors: Assoc.Prof.Dr.habil. Vu Hoang Linh and Prof.Dr. Nguyen Huu Du

11. Summary of the new findings of the thesis

In this thesis, we have investigated the stability  and robust stability of linear singular systems of difference equations of first order.

The stability of systems has been analyzed when the coefficients are subject to perturbations;

Three Bohl-Perron-type stability theorems have been obtained for singular difference equations of index-1;

The notion of Bohl exponent has been extended to linear singular systems of difference equations and its properties have been presented.

We have also investigated a class of linear time-varying singular systems of second order difference equations by the strangeness-index approach.

The solvability of initial value problems as well as the construction of consistent initial conditions have been discussed;

Some criteria for exponential stability have been established and a Bohl-Perron-type stability theorem has been presented.

Bounds for allowable perturbations have been obtained so that the perturbed systems preserve the index as well as the exponential stability.

12. Practical applicability, if any: Stability and robust stability of linear singular difference equation can be applied to practical problems such as control theory, analysis of mathematical models in biology and economics …

13. Further research directions, if any:

As future works toward the complete analysis of general singular discrete-time systems of high order, a theory of strangeness index and a reduction procedure like those for first order systems and those for delay differential algebraic equations should be done, with which we can transform an arbitrary general system into the strangeness-free form under certain assumptions. A complete theory of Lyapunov, Bohl, and Sacker-Sell spectra for singular difference equations would be an interesting project, as well.

14. Thesis-related publications:

[1] Nguyen Huu Du, Vu Hoang Linh and Ngo Thi Thanh Nga (2016), “On stability and Bohl exponent of linear singular systems of difference equations with variable coefficients”,  J. Differ. Equations Appl., 22, pp.1350-1377.

[2] Vu Hoang Linh, Ngo Thi Thanh Nga (2018), “Bohl–Perron Type Stability Theorems for Linear Singular Difference Equations”,  Vietnam J. Math., 46, pp.437-451.

[3] Vu Hoang Linh, Ngo Thi Thanh Nga, Do Duc Thuan (2018), “Exponential stability and robust stability for linear time-varying singular systems of second-order difference equations”, SIAM J. Matrix Anal. Appl., 39-1, pp.204-233.