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


[ 1 ] Instytut Elektrotechniki i Elektroniki Przemysłowej, Wydział Elektryczny, Politechnika Poznańska | [ 2 ] Instytut Elektrotechniki i Elektroniki Przemysłowej, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ E ] pensioner

Year of publication


Published in

Poznan University of Technology Academic Journals. Electrical Engineering

Journal year: 2020 | Journal number: no. 104

Article type

scientific article

Publication language


  • state equation
  • solutions of state equations
  • algebraic forms

EN 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.

Pages (from - to)

75 - 86

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