Controllability of conservative behaviours

• Published in: International journal of control Vol. 85; no. 8; pp. 983 - 989
• Main Author: Rao, Shodhan
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.08.2012; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applied sciences; Behavior; behavioural systems theory; Computer science; control theory; systems; conservative behaviours; Control system analysis; Control theory. Systems; Controllability; Electric networks; Exact sciences and technology; input cardinality; Lossless; output cardinality; quadratic differential forms; Stability; Studies; System theory; Input output; Lossless circuit; Polynomial matrix; Differential form; input cardinality: output cardinality; quadratic differential forms; Systems theory; Symmetric polynomial; behavioural systems theory; conservative behaviours; Electrical network; Behavioral analysis; Symmetric matrix; Controllability; Matrix polynomial; Quadratic form
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2012.673134

In this article, we first define the class of J-conservative behaviours with observable storage functions, where J is a symmetric two-variable polynomial matrix. We then provide two main results. The first result states that if J(−ξ, ξ) is nonsingular, the input cardinality of a J-conservative behaviour with an observable storage function is always less than or equal to its output cardinality. The second result states that if J is constant and nonsingular, a J-conservative behaviour with an observable storage function and equal input and output cardinalities is always controllable. Physically the second result implies that a class of multiport lossless electrical networks is controllable.