Realizacje dodatnie stabilne liniowych układów ciągłych niecałkowitego rzędu z macierzą systemową symetryczną Metzlera

• Autorzy: Kaczorek T. , Borawski K.

Warianty tytułu

EN

Positive stable realization problem for linear continuous-time fractional-order systems with symmetric system Metzler matrix

• Języki publikacji: PL

Abstrakty

PL

Podano warunki dodatniości i stabilności liniowych układów ciągłych niecałkowitego rzędu. Sformułowano problem realizacji dodatnich stabilnych liniowych układów ciągłych niecałkowitego rzędu z macierzą systemową symetryczną Metzlera. Zaproponowano metodę sprowadzania macierzy stanu w postaci kanonicznej Frobeniusa do postaci symetrycznej stabilnej Metzlera. Metodę zobrazowano przykładem numerycznym.

EN

A dynamical system is called a fractional-order system if its state equations are given by fractional-order derivative of the state vector. Using that theory, more precise mathematical models of systems can be obtained. A dynamical system is called positive if its all inputs, outputs, state variables and initial conditions are nonnegative. Variety of models having positive behavior can be found in engineering, biology, economics etc. Conditions for positivity and stability of linear continuous-time fractional-order systems are presented in the paper. A positive stable realization problem for linear continuous-time fractional-order systems with symmetric system Metzler matrix is formulated. The method for finding the realization is given. The problem is solved and conditions for the existence of the realization are established. The paper is organized as follows. In Section 2 the conditions for internal positivity and stability of linear continuous-time fractional-order systems are given. This section also contains the formulation of the positive stable realization problem for linear continuous-time fractional-order systems with symmetric system Metzler matrix. In Section 3 the procedure for computation of the realization is given. An example illustrating the method proposed is presented in Section 4. Section 5 contains the concluding remarks.

Słowa kluczowe

PL

liniowy układ ciągły niecałkowitego rzędu; realizacja dodatnia stabilna; macierz symetryczna; macierz Metzlera

EN

linear continuous-time fractional-order system; positive stable realization; symmetric matrix; Metzler matrix

• Wydawca: Wydawnictwo PAK
• Czasopismo: Pomiary Automatyka Kontrola
• Rocznik: 2014
• Tom: R. 60, nr 10
• Strony: 822--825
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Kaczorek T.

• Politechnika Białostocka, Wydział Elektryczny, ul. Wiejska 45d, 15-351 Białystok

autor

Borawski K.

• Politechnika Białostocka, Wydział Elektryczny, ul. Wiejska 45d, 15-351 Białystok

Bibliografia

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