Every storage function is a state function

Systems and Control Letters

Volumn 32, Issue 5, 1997, Pages 249-259

  Trentelman, H L ^a   Willems, J C ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Dissipative dynamical systems; Quadratic differential forms; State; Storage function; Two variable polynomial matrices

Indexed keywords

EID: 0000246216     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(97)00081-9     Document Type: Article

References (13)

1. F.M. Callier, On polynomial spectral factorization by symmetric extraction, IEEE Trans. Automat. Control 30 (1985) 453-464.
2. W.A. Coppel, Linear Systems, Notes in Pure Mathematics, vol. 6, Australian National University, 1972.
3. C.A. Desoer, E.S. Kuh, Basic Circuit Theory, McGraw-Hill, Tokyo, 1969.
4. D.J. Hill, P.J. Moylan, Stability of nonlinear dissipative systems, IEEE Trans. Automat. Control 21 (1976) 708-711.
5. M. Kuijper, First-order Representations of Linear Systems, Birkhäuser, Boston, 1994.
6. P. Rapisarda, J.C. Willems, State maps for linear systems, SIAM J. Control Optim. 35 (1997) 254-264.
7. H.L. Trentelman, J.C. Willems, The dissipation inequality and the algebraic Riccati equation, in: S. Bittanti, A.J. Laub, J.C. Willems (Eds.), The Riccati Equation, Springer, Berlin, 1991, pp. 197-242.
8. J.C. Willems, Dissipative dynamical systems - Part I: general theory, Part II: linear systems with quadratic supply rates, Arch. Rat. Mech. Anal. 45 (1972) 321-351 and 352-393.
9. J.C. Willems, From time series to linear system. Part I: finite dimensional linear time invariant systems; Part II: exact modelling, Part III: approximate modelling, Automatica 22 (1986) 561-580 and 675-694; 23 (1987) 87-115.
10. J.C. Willems, From time series to linear system. Part I: finite dimensional linear time invariant systems; Part II: exact modelling, Part III: approximate modelling, Automatica 22 (1986) 561-580 and 675-694; 23 (1987) 87-115.
11. J.C. Willems, Models for dynamics, Dynamics Reported 2 (1989) 171-269.
12. J.C. Willems, Paradigms and puzzles in the theory of dynamical systems, IEEE Trans. Automat. Control 36 (1991) 259-294.
13. J.C. Willems, H.L. Trentelman, On quadratic differential forms, SIAM J. Control Optim., to appear.