Storage functionals and Lyapunov functions for passive dynamical systems

• Autorzy: Borukhov V. , Shnip A. , Zelenyak D.
• Języki publikacji: EN

Abstrakty

EN

For nonlinear time-invariant input-output dynamical systems the passivity conditions are obtained under some restrictions. The conditions imply storage functions satisfying dissipation inequality. A class of storage functions allowing unique reconstruction of a passive dynamical system is defined. These results are illustrated by an example of a linear system with fading memory. An important, for practical application, class of the linear relaxation systems without direct input-output interaction is considered. A new necessary condition for dynamical systems to be of the relaxation type is obtained for this class. The condition is connected with the existence of a unique quadratic Lyapunov function satisfying the complete monotonicity condition. This unique Lyapunov function corresponds to a "standard" thermodynamic potential in a compact family of potentials in the non-equilibrium thermodynamics. The results obtained can be useful in automatic control, mechanics of viscoelastic materials, and various applications in physics and the system theory.

Słowa kluczowe

EN

linear systems; linear relaxation systems; passive dynamical systems; nonlinear control systems

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2001
• Tom: Vol. 27, nr 2
• Strony: 27--35
• Opis fizyczny: Bibliogr. 5 poz.,

Twórcy

autor

Borukhov V.

autor

Shnip A.

autor

Zelenyak D.

• Institute of Mathematics, Academy of Sciences of Belarus, Surganov Str., 11, 220072 Minsk, Belarus