Dissertation of Doctor of Philosophy in Mathematics

The thesis "Stability of some classes of degenerate two-phase difference systems with delay" is to study the stability of degenerate two-phase systems with mixed delay in the direction of variation; Stability and dissipation in finite domain of degenerate 2-D system with variable delay; Evaluation of the gain set and control design for a degenerate 2-D system in the Roesser model with variable delay;... Please refer to it!

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The dissertation is written on the basis of the paper published in Annales Polonici Mathematici, the paper published in Acta Mathematica Vietnamica and the paper published in Results in Mathematics.

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In the dissertation, we consider the problem of finding the shortest path between two points along a sequence of adjacent triangles in a general setting. The sequence of triangles is replaced by a sequence of ordered line segments. The 3D space is replaced by a Euclidean space.

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The research related to this dissertation was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) and Hanoi National University of Education.

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Objectives: The main objective of this thesis is to study the problem of stability analysis and applications in control of discrete-time 2-D systems described by Roesser model with certain types of stochastic parameters. The research includes the methodology development and establishment of analysis and synthesis conditions of the following specified models.

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An important chapter in the theory of distribution of zeros of entire functions pertains to the study of linear operators acting on entire functions. This dissertation presents new results involving not only linear, but also some non-linear operators.

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