论文信息 - Dissipative Distributed Systems

Dissipative Distributed Systems

Deals with systems described by constant coefficient linear partial differential equations. We define dissipativity with respect to a quadratic differential form, i.e., a quadratic functional in the system variables and their partial derivatives. The main result states the equivalence of dissipativity and the existence of a storage function or of a dissipation rate.

Harish K. Pillai | Jan C. Willems

[1] U. Oberst. Multidimensional constant linear systems , 1990, EUROCAST.

[2] L.C.G.J.M. Habets,et al. Book review: Introduction to mathematical systems theory, a behavioral approach , 2000 .

[3] J. Willems,et al. Synthesis of dissipative systems using quadratic differential forms: part II , 2002, IEEE Trans. Autom. Control..

[4] Jan C. Willems,et al. Models for Dynamics , 1989 .

[5] Harish K. Pillai,et al. A Behavioral Approach to Control of Distributed Systems , 1999 .

[6] J. Willems. Dissipative dynamical systems part I: General theory , 1972 .

[7] Jan C. Willems,et al. Introduction to mathematical systems theory: a behavioral approach, Texts in Applied Mathematics 26 , 1999 .

[8] T. Glad,et al. An Algebraic Approach to Linear and Nonlinear Control , 1993 .

[9] J. Willems,et al. On Quadratic Differential Forms , 1998 .

[10] M. Fliess,et al. Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[11] U. Oberst,et al. Continuous-varying linear systems , 1998 .

[12] Jean-François Pommaret,et al. Localization and parametrization of linear multidimensional control systems , 1999 .

[13] J. Willems. Paradigms and puzzles in the theory of dynamical systems , 1991 .

[14] Jean-François Pommaret. Partial Differential Equations and Group Theory: New Perspectives for Applications , 2014 .