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Representation of Solutions of Linear Discrete Systems with Delay
Morávková, Blanka ; Růžičková, Miroslava (oponent) ; Khusainov, Denys (oponent) ; Diblík, Josef (vedoucí práce)
The dissertation thesis is concerned with linear discrete systems with constant matrices of linear terms with a single or two delays. The main objective is to obtain formulas analytically describing exact solutions of initial Cauchy problems. To this end, some matrix special functions called discrete matrix delayed exponentials are defined and used. Their basic properties are proved. Such special matrix functions are used to derive analytical formulas representing the solutions of initial Cauchy problems. First is discussed the initial problem with impulses are acting at some prescribed points and formulas describing the solutions of this problem are derived. In the next part of the dissertation, two definitions of discrete matrix delayed exponentials for two delays are given and their basic properties are proved. Such discrete special matrix functions make it possible to find representations of solutions of linear systems with two delays. This is done in the last part of dissertation thesis where two different formulas giving the analytical solution of this problem are derived.
Representation of Solutions of Linear Discrete Systems with Delay
Morávková, Blanka ; Růžičková, Miroslava (oponent) ; Khusainov, Denys (oponent) ; Diblík, Josef (vedoucí práce)
The dissertation thesis is concerned with linear discrete systems with constant matrices of linear terms with a single or two delays. The main objective is to obtain formulas analytically describing exact solutions of initial Cauchy problems. To this end, some matrix special functions called discrete matrix delayed exponentials are defined and used. Their basic properties are proved. Such special matrix functions are used to derive analytical formulas representing the solutions of initial Cauchy problems. First is discussed the initial problem with impulses are acting at some prescribed points and formulas describing the solutions of this problem are derived. In the next part of the dissertation, two definitions of discrete matrix delayed exponentials for two delays are given and their basic properties are proved. Such discrete special matrix functions make it possible to find representations of solutions of linear systems with two delays. This is done in the last part of dissertation thesis where two different formulas giving the analytical solution of this problem are derived.

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1 Morávková, Barbora
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