Abstract
The theory of balanced realizations is essentially based on co-ordinating controllability and observability properties of a finite dimensional linear asymptotically stable system. By analyzing more general quadratic measures on the external behaviour of a dynamical system, we may obtain state space representations in which other quantities are internally balanced. For the class of L 2-trajectories of finite dimensional linear time invariant systems, we formalize the notion of a balanced state space with respect to these type of quadratic measures. A particular choice of quadratic measures is studied in more detail and it is shown that ‘classical’ balanced realizations are obtained as a special case.KeywordsBalanced realizationsfinite dimensional linear time invariant systemsstate space methodsmodel approximation
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