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.

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

autor

Shnip A.

• A.V. Luikov Heat and Mass Transfer Institute, P. Brovka Str., 15, Minsk, Belarus

autor

Zelenyak D.

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

Bibliografia

• [1] BORUKHOV V. T., On the dissipative inequality for finite-dimensional linear passive dynamical systems, Differential Equations, Vol. 35, No. 1, 1999, 14-22.
• [2] BORUKHOV V. T., SHNIP A. I., On the dissipative inequality for non-linear passive dynamical input output systems, Dokl. Nats. Akad. Nauk Belarusi, Vol. 43, No. 6, 1999, 13-17.
• [3] BORUKHOV V. T., SHNIP A. I., Subordinated systems and dissipative inequality for linear finite dimensional passive systems, Systems Science, Vol. 25, No. 4, 1999, 15-24.
• [4] WILLEMS J. C., Realization of systems with internal passivity and symmetry constraints, Journ. of Franclin Inst., Vol. 301, No. 6, 1978, 605-621.
• [5] WILLEMS J. C., Dissipative dynamical systems. Part II: linear systems with quadratic supply rates, Arch. Rational Meeh. Anal., 1972, Vol. 45, 352-393.