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Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities
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DOI：10.1016/j.automatica.2003.07.001.png)
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Abstract
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Randomized algorithms are proposed for solving parameter-dependent linear matrix inequalities and their computational complexity is analyzed. The first proposed algorithm is an adaptation of the algorithms of Polyak and Tempo [(Syst. Control Lett. 43(5) (2001) 343)] and Calafiore and Polyak [(IEEE Trans. Autom. Control 46 (11) (2001) 1755)] for the present problem. It is possible however to show that the expected number of iterations necessary to have a deterministic solution is infinite. In order to make this number finite, the improved algorithm is proposed. The number of iterations necessary to have a probabilistic solution is also considered and is shown to be independent of the parameter dimension. A numerical example is provided. (C) 2003 Elsevier Ltd. All rights reserved.
Keywords:
randomized algorithms
parameter-dependent linear matrix inequalities
computational complexity
conservatism
curse of dimensionality
linear parameter-varying systems
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