Stabilność asymptotyczna według składowych i stabilność wykładnicza dodatnich dyskretnych układów liniowych niecałkowitego rzędu

• Autorzy: Kaczorek T. , Cimochowski R.

Warianty tytułu

EN

Componentwise asymptotic stability and exponential stability of the positive fractional discrete-time linear systems

• Języki publikacji: PL

Abstrakty

PL

Podano podstawowe definicje i twierdzenia dotyczące dodatnich układów dyskretnych niecałkowitego rzędu oraz omówiono ich stabilność asymptotyczną. Podano warunki konieczne i wystarczające stabilności asymptotycznej według składowych i stabilności wykładniczej dodatnich układów dyskretnych niecałkowitego rzędu. Przedstawiono przykłady numeryczne ilustrujące problem stabilności asymptotycznej według składowych i stabilności wykładniczej.

EN

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear systems behaviour can be found in engineering, management science, economics, social sciences, biology and medicine, etc. Positive linear systems are defined on cones and not on linear spaces. Therefore, the theory of positive systems is more complicated and less advanced. The concept of positive fractional discrete-time linear systems has been introduced in [6] and the reachability and controllability to zero of positive fractional system has been investigated in [10]. In this paper the problem of the componentwise asymptotic stability and exponential stability of the positive fractional systems will be solved. The paper is organized as follows. In section 2 the basic definitions and theorems concerning the positive fractional systems are recalled and their asymptotic stability is discussed. The main result of the paper is presented in section 3 and 4. Necessary and sufficient conditions for the componentwise asymptotic stability and exponential stability of the positive fractional systems are established. The considerations are illustrated by numerical examples in section 5. The algorithm in MATLAB, which allows the test of the componentwise asymptotic stability and exponential stability of the positive fractional systems is presented. How does presented procedure work is step-by step described. In section 6 the relationship between the componentwise asymptotic stability and exponential stability is presented. Concluding remarks and open problems are given in section 7.

Słowa kluczowe

PL

liniowe układy dyskretne niecałkowitego rzędu; dodatniość; stabilność asymptotyczna według składowych; stabilność wykładnicza

EN

linear discrete time fractional systems; positivity; componentwise asymptotic stability; exponential stability

• Wydawca: Wydawnictwo PAK
• Czasopismo: Pomiary Automatyka Kontrola
• Rocznik: 2010
• Tom: R. 56, nr 5
• Strony: 414--417
• Opis fizyczny: Bibliogr. 24, wzory

Twórcy

autor

Kaczorek T.

autor

Cimochowski R.

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

Bibliografia

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