Controllability of conservative behaviours

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.