Abstract
A method allowing a desirable matrix spectrum to be constructed as an alternative to the method using matrix transformation to the Frobenius form is stated. It can be applied to implement control algorithms for technical systems without executing the variables transformation procedures that are needed for deriving a Frobenius matrix. The method can be used for simulation of systems with different spectrums for choosing an alternative that satisfies to the distinct demands.
Highlights
A number of mathematical problems deal with changes of a matrix spectrum [1,2]
A method allowing a desirable matrix spectrum to be constructed as an alternative to the method using matrix transformation to the Frobenius form is stated
It can be applied to implement control algorithms for technical systems without executing the variables transformation procedures that are needed for deriving a Frobenius matrix
Summary
A number of mathematical problems deal with changes of a matrix spectrum [1,2]. It can be changed by various methods, for example, in computing problems, a multiplication to other matrix is used. To change a spectrum, a matrix is added with some other matrix derivated by a feedback, which forms a linear function of variables. This approach is known as modal control [3,4] or spectrum control [5]. In order to obtain a Frobenius matrix it is necessary to transform physical variables of feedback loop In this case the transformation is double, because just a combination of physical variables must goes to the input. The method of obtaining a desirable spectrum without resort to a Frobenius matrix is stated It can be used for calculating the feedback coefficients of a control system for the purpose to derive a desirable spectrum. Among them the most demanded for practical applications it is possible to consider the spectrum correction problem, when it is required to determine parameters of a feedback for altering a part of a spectrum
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