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1 Poznan University of Technology Academic Journals. Electrical Engineering

1 2020

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Algebraic forms of solutions of linear state equations for determined control vectors

Porada Ryszard, Mielczarek Norbert

Poznan University of Technology Academic Journals. Electrical Engineering

2020

No. 104

75--86

Despite intensive development of numerical methods of resolution of ordinary differential equations, we still seek analytical solutions of these equations in the algebraic form. The analytical solution in an algebraic form, is very convenient in case of investigation of the course of solution in a large interval of changes of parameters, it also gives more qualitative informations. This concerns first of all linear equations which are the most often met models of physical objects. Important advantage of these solutions is also their open form regarding established state of the system. The paper proves existence of algebraic forms of solutions of control vectors with components: exponential, sinusoidal with different circular frequencies and sinusoidal multiple. Also solutions for other kind of control vectors which are mentioned in the literature are presented.