TY - JOUR
T1 - Introduction to Jan C. Willems', 'Dissipative Dynamical Systems, Part II
T2 - Linear Systems with Quadratic Supply Rates'
AU - Van Der Schaft, Arjan
N1 - Publisher Copyright:
© 1991-2012 IEEE.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - The two-part article, 'Dissipative Dynamical Systems,' by Jan C. Willems, was submitted in January 1972 to the Archive for Rational Mechanics and Analysis and published in the same year (vol. 45, Part I, pp. 321-351, Part II: pp. 352-393). While Part I develops the theory of dissipative systems for general input-state-output systems, Part II confines itself to linear systems. Moreover, most of Part II is about dissipativity with respect to the supply rate y{\hspace{0.06em}}{\top}u, that is, linear passive systems. The main questions addressed in Part II concern the analysis of the set of storage functions of linear passive systems (with the existence of a minimal and maximal element already established in Part I) and the compatibility of storage functions with other external and internal symmetry properties of the system, such as reciprocity and reversibility. (See 'The Articles of This Special Issue.') This links the article closely to the realization theory of physical linear systems, in particular, the network synthesis of electrical circuits, the Onsager-Casimir relation of linear thermodynamics, and the input-output analysis of linear viscoelastic systems.
AB - The two-part article, 'Dissipative Dynamical Systems,' by Jan C. Willems, was submitted in January 1972 to the Archive for Rational Mechanics and Analysis and published in the same year (vol. 45, Part I, pp. 321-351, Part II: pp. 352-393). While Part I develops the theory of dissipative systems for general input-state-output systems, Part II confines itself to linear systems. Moreover, most of Part II is about dissipativity with respect to the supply rate y{\hspace{0.06em}}{\top}u, that is, linear passive systems. The main questions addressed in Part II concern the analysis of the set of storage functions of linear passive systems (with the existence of a minimal and maximal element already established in Part I) and the compatibility of storage functions with other external and internal symmetry properties of the system, such as reciprocity and reversibility. (See 'The Articles of This Special Issue.') This links the article closely to the realization theory of physical linear systems, in particular, the network synthesis of electrical circuits, the Onsager-Casimir relation of linear thermodynamics, and the input-output analysis of linear viscoelastic systems.
UR - http://www.scopus.com/inward/record.url?scp=85131678497&partnerID=8YFLogxK
U2 - 10.1109/MCS.2022.3157114
DO - 10.1109/MCS.2022.3157114
M3 - Article
AN - SCOPUS:85131678497
SN - 1066-033X
VL - 42
SP - 32
EP - 35
JO - IEEE Control Systems Magazine
JF - IEEE Control Systems Magazine
IS - 3
ER -