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Linear Matrix Differential Equation with Delay
Piddubna, Ganna Konstantinivna ; Růžičková, Miroslava (oponent) ; Dzhalladova, Irada (oponent) ; Baštinec, Jaromír (vedoucí práce)
This work is devoted to computing the solution, stability of the solution and controllability of respective system of linear matrix differential equation with delay x'(t)=A0x(t)+A1 x(t-tau), where A0, A1 are constant matrices and tau>0 is the constant delay. To solve this equation, the "step by step" method was used. The solution was found in recurrent form and in general form. Stability and the asymptotic stability of the solution of the equation was investigated. Conditions for stability were defined. The Lyapunov’s functional theory is basic for the investigation. Necessary and sufficient condition for controllability in same matrices case was defined and the control was built. Sufficient conditions for controllability in communicative matrices case and general case were defined and controls were built. All results were illustrated with non-trivial examples.
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Lineární teorie diferenciálních rovnic se zpožděním
Marková, Hana ; Pražák, Dalibor (vedoucí práce) ; Kaplický, Petr (oponent)
Tato práce se zabývá studiem zpožděných diferenciálních funkcionálních rovnic. Z Banachovy věty o pevném bodě plyne existence jednoznačného řešení, ale už žádná infor- mace o tom, jak vypadá. V práci se zaměřujeme právě na toto vyjádření, kterého docílíme pomocí aplikace Laplaceovy transformace na obě strany rovnice. Tedy řešíme modifiko- vaný problém, na jehož řešení následně aplikujeme inverzní Laplaceovu transformaci k vyjádření řešení původního problému. Na konci práce ještě formulujeme a dokazujeme nejlepší exponenciální odhad řešení. 1
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Linear Matrix Differential Equation with Delay
Piddubna, Ganna Konstantinivna ; Růžičková, Miroslava (oponent) ; Dzhalladova, Irada (oponent) ; Baštinec, Jaromír (vedoucí práce)
This work is devoted to computing the solution, stability of the solution and controllability of respective system of linear matrix differential equation with delay x'(t)=A0x(t)+A1 x(t-tau), where A0, A1 are constant matrices and tau>0 is the constant delay. To solve this equation, the "step by step" method was used. The solution was found in recurrent form and in general form. Stability and the asymptotic stability of the solution of the equation was investigated. Conditions for stability were defined. The Lyapunov’s functional theory is basic for the investigation. Necessary and sufficient condition for controllability in same matrices case was defined and the control was built. Sufficient conditions for controllability in communicative matrices case and general case were defined and controls were built. All results were illustrated with non-trivial examples.
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