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Principle of Argument Increment For Searching Polynomial Roots
Tošer, Pavel ; Tofel, Pavel (referee) ; Sadovský, Petr (advisor)
Several methods exist for searching multinominal roots. Methods in more cases are used only for special solves. The goal of this thesis is to discover solution for searching multinominal roots. The process is based on optimal iterative method in combination with priciple of argument increment. There is no procedure solving it in this way up to now. This method removes shortcomings already existing methods and she could also complement them with a new knowledge.
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Optimization in control systems
Daniel, Martin ; Václavek, Pavel (referee) ; Pohl, Lukáš (advisor)
Master’s thesis deals with using a linear matrix inequality (LMI) in control of a dynamic systems. We can define a stability of a dynamic system with a LMI. We can use a LMI for research if the poles of a system are in a given regions in the left half-plane of the complex plane with a LMI or we can use a LMI for a state feedback control. In the work we describe a desing of a controller minimizing a norm from an input to an output of the system. There is also a desing of a LQ controller with a LMI. In the end of the work, there are two examples of a design a LQ controller, which minimize the norm from the input to the output of the system and moves a poles of a dynamic system in a given regions in the complex plane, with the LMI. We use a LMI for a design a continuos LQ controller in the first example. In the second example we use a LMI for a design a discrete LQ controller.
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Stability of a bar influenced by small and large imperfections
Náprstek, Jiří ; Fischer, Cyril
The geometrical and physical imperfections of systems can drastically reduce their critical loading. These imperfections are usually of stochastic character and, therefore, they act as random parametric perturbations of coefficients of corresponding differential equations. In this paper, the imperfections are introduced as multidimensional statistics on the set of a large number of realizations of the same system. As far as the amount of information is small or the imperfections themselves cannot be considered small, the convex analysis is preferable. The paper compares results obtained by both stochastic and convex analyses for hyperprism and demonstrates when each of them is more convenient to be used. Besides of the hyper-prism, the possibilities and properties of other modifications of convex method are considered, especially those based on the definition of imperfection zone marked as a centric hyper-ellipsoid or as an eccentric hyper-ellipsoid. The analytical background was brought up to the level when only a few configurations of imperfections are sufficient to be evaluated numerically. These configurations are obtained by means of the convex analysis as points of extreme critical loading using the Lagrange method of constrained extremes.
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Optimization in control systems
Daniel, Martin ; Václavek, Pavel (referee) ; Pohl, Lukáš (advisor)
Master’s thesis deals with using a linear matrix inequality (LMI) in control of a dynamic systems. We can define a stability of a dynamic system with a LMI. We can use a LMI for research if the poles of a system are in a given regions in the left half-plane of the complex plane with a LMI or we can use a LMI for a state feedback control. In the work we describe a desing of a controller minimizing a norm from an input to an output of the system. There is also a desing of a LQ controller with a LMI. In the end of the work, there are two examples of a design a LQ controller, which minimize the norm from the input to the output of the system and moves a poles of a dynamic system in a given regions in the complex plane, with the LMI. We use a LMI for a design a continuos LQ controller in the first example. In the second example we use a LMI for a design a discrete LQ controller.
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Principle of Argument Increment For Searching Polynomial Roots
Tošer, Pavel ; Tofel, Pavel (referee) ; Sadovský, Petr (advisor)
Several methods exist for searching multinominal roots. Methods in more cases are used only for special solves. The goal of this thesis is to discover solution for searching multinominal roots. The process is based on optimal iterative method in combination with priciple of argument increment. There is no procedure solving it in this way up to now. This method removes shortcomings already existing methods and she could also complement them with a new knowledge.
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