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Positive extremal values and solutions of the exponential equations with application to automatics

100%

Górecki H. , Zaczyk M. , Górecki H. , Zaczyk M.

Positive extremal values and solutions of the exponential equations with application to automatics

100%

Górecki H. , Zaczyk M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2020

tom Vol. 68, nr 3

585--591

In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. There are obtained the analytical solutions of the equations and also the maximal positive values of these solutions. The obtained sufficient conditions of the positivity of these solutions are defined by the Theorems. There are also formulated the necessary conditions of the positivity of these solutions. The analytical formulae enable the design of the system with prescribed properties.

Analytic solution of transcendental equations

100%

Górecki H.

International Journal of Applied Mathematics and Computer Science

2010

tom 20

nr 4

671-677

A decomposition technique of the solution of an n-th order linear differential equation into a set of solutions of 2-nd order linear differential equations is presented.

Analytic solution of transcendental equations

75%

Górecki H.

International Journal of Applied Mathematics and Computer Science

2010

tom Vol. 20, no 4

671-677

A decomposition technique of the solution of an n-th order linear differential equation into a set of solutions of 2-nd order linear differential equations is presented.

Analityczne wyznaczanie ekstremów i zer równań różniczkowych n-tego rzędu

75%

Górecki H.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

2009

tom T. 13, z. 2

275-288

W pracy przedstawiono metodę wyznaczania ekstremów rozwiązań równań różniczkowych liniowych o stałych współczynnikach, rzędu trzeciego i wyższych.

A method for determination the extrema of solutions of linear differential equations with constant coefficients of the third and higher orders.

A new method for analytic determination of extremum of the transients in linear systems

51%

Górecki H.

Control and Cybernetics

2004

tom Vol. 33, no 2

275-295

The relation between extremal values of the error and the coefficients of its differential equations is one of the central problems of control systems in chemical industry, because extremal values of the error sometimes cause serious damages to the environment or to the system itself. Analytical formulae for the determination of these values are known only for the second-order systems. In this paper a method which permits to determine extremal values of the error in higher-order systems is proposed.