Rational orthonormal bases, state transformations, and dissipativity

We establish formulas relating the state of a continuous-time system with that of the transformed one in a Takenaka-Malmquist-Kautz orthogonal basis. We use such relation to give a simple proof that if the original system is dissipative, then the transformed one is also dissipative with the same storage function. We apply our results to continuous-time subspace system identification.