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arXiv · 2502.21102

Minimal positive Markov realizations

Hamed Taghavian·Jens Sjölund
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Abstract

Finding a positive state-space realization with the minimum dimension for a given transfer function is an open problem in control theory. In this paper, we focus on positive realizations in Markov form and propose a linear programming approach that computes them with a minimum dimension. Such minimum dimension of positive Markov realizations is an upper bound of the minimal positive realization dimension. However, we show that these two dimensions are equal for certain systems.

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Hamed Taghavian, Jens Sjölund. 2025-02-28. Minimal positive Markov realizations. https://arxiv.org/abs/2502.21102

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