Maintainability of positive linear discrete-time systems

• Autorzy: James G. , Rumchev V.
• Języki publikacji: EN

Abstrakty

EN

The concept of maintainability for (time-invariant) positive linear discrete-time systems (PLDS) is introduced and studied in detail. A state x(t) of a PLDS is said to be maintainable if there exists an admissible control such that x(t + 1) = x(t) for t = 0, 1, 2, ... For time-invariant systems, if a given state is maintainable it is maintainable at all times. The set of all maintainable states is called a maintainable set. Maintainability and stability are different concepts - while stability is an asymptotic ("long-term") notion, maintainability is a "short-term" concept. Moreover, stability always implies maintainability but maintainability does not necessarily imply stability. If no additional constraints are imposed on the states and controls except the standard non-negativity restrictions, the maintainable sets are polyhedral cones. Their geometry is determined completely by the structural and spectral properties of nonnegative system pair (A, B) ≥ 0. Different cases are studied in the paper and relevant numerical examples are presented. PLDS with two-side bounded controls are also discussed and an interesting result is obtained namely the maintainable set of an asymptotically stable PLDS coincides with its asymptotic reachable set.

Słowa kluczowe

EN

linear systems; positive systems; discrete-time; maintainability; equilibrium sets; reachable set; non-negative matrices

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2007
• Tom: Vol. 33, no 3
• Strony: 21--30
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

James G.

autor

Rumchev V.

• Control Theory and Applications Centre, Coventry University, CV1 5FB, CV1 5FB Coventry, UK,

Bibliografia

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