Positive feedback interconnection of Hamiltonian systems

Recent results on counterclockwise input-output dynamics and negative-imaginary transfer matrices are interpreted from a geometric Hamiltonian systems point of view, providing additional insights and results.

[1]  P J Fox,et al.  THE FOUNDATIONS OF MECHANICS. , 1918, Science.

[2]  C. Wall.  Geometric properties of generic differentiable manifolds , 1977 .

[3]  Shlomo Sternberg,et al.  Some Problems in Integral Geometry and Some Related Problems in Micro-Local Analysis , 1979 .

[4]  Jerrold E. Marsden,et al.  Foundations of Mechanics: 2nd Edition , 1980 .

[5]  R. Brockett,et al.  Foundations of mechanics, 2nd edition , 1981, IEEE Transactions on Automatic Control.

[6]  A. Schaft.  Observability and Controllability for Smooth Nonlinear Systems , 1982 .

[7]  A. J. van der Schaft,et al.  Symmetries, conservation laws, and time reversibility for Hamiltonian systems with external forces , 1983 .

[8]  Y. Egorov,et al.  Fourier Integral Operators , 1994 .

[9]  A. Schaft,et al.  The Hamiltonian formulation of energy conserving physical systems with external ports , 1995 .

[10]  A. Schaft.  L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[11]  Arjan van der Schaft,et al.  Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems , 2002, Autom..

[12]  D. Angeli,et al.  On systems with counter-clock-wise input/output dynamics , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[13]  Arjan van der Schaft,et al.  Hamiltonian dynamics with external forces and observations , 1981, Mathematical systems theory.

[14]  JinHyoung Oh,et al.  Counterclockwise Dynamics of a Rate-Independent Semilinear Duhem Model , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[15]  David Angeli,et al.  Systems with counterclockwise input-output dynamics , 2006, IEEE Transactions on Automatic Control.

[16]  David Angeli,et al.  Multistability in Systems With Counter-Clockwise Input–Output Dynamics , 2007, IEEE Transactions on Automatic Control.

[17]  Ian R. Petersen,et al.  Stability Robustness of a Feedback Interconnection of Systems With Negative Imaginary Frequency Response , 2008, IEEE Transactions on Automatic Control.

[18]  Arjan van der Schaft,et al.  A Port-Hamiltonian Formulation of Open Chemical Reaction Networks , 2010 .

[19]  Alexander Lanzon,et al.  Feedback Control of Negative-Imaginary Systems , 2010, IEEE Control Systems.

[20]  Ian R. Petersen,et al.  A Negative Imaginary Lemma and the Stability of Interconnections of Linear Negative Imaginary Systems , 2010, IEEE Transactions on Automatic Control.

[21]  Jean Lévine,et al.  Advances in the Theory of Control, Signals and Systems with Physical Modeling , 2011 .