Kalle M. Mikkola

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We obtain state-space formulas for the solution of the Nehari-Takagi/sub-optimal Hankel norm approximation problem for infinite-dimensional systems with a nonexponentially stable generator, via the method of J-spectral factorization. We make key use of a purely frequency domain solution of the problem. Acknowledgements: This work was completed during a stay(More)
It is known that a matrix-valued transfer function P has a stabilizing dynamic controller Q (i.e., h I −Q −P I i −1 ∈ H ∞) iff P has a right (or left) coprime factorization. We show that the same result is true in the operator-valued case. Thus, the standard Youla–Bongiorno parameteriza-tion applies to every dynamically stabilizable function. We then derive(More)
We formulate a minimax game which is equivalent to the Nehari problem in the sense that this minimax game is well-posed if and only if the Hankel norm of a given operator is less than a prescribed constant. This game and the dual game provide us with physical interpretations of the Riccati operators that are commonly used in the solution of the Nehari(More)
We compute the Bass stable rank and the topological stable rank of several convolution Banach algebras of complex measures on (−∞, ∞) or on [0, ∞) consisting of a discrete measure (modelling delays, possibly commensurate or having n generators) and/or of an absolutely continuous measure (an L 1 function). We also compute the stable ranks of the convolution(More)
During the past decades much of finite-dimensional systems theory has been generalized to infinite dimensions. However, there is one important flaw in this theory: it only guarantees complex solutions, even when the data is real. We show that the standard solutions of many classical problems with real data are also real. We call a (possibly matrix-or(More)