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Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities |
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| Authors: | Yasuaki Hidenori |
| Affiliation: | a Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan b Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan |
| Abstract: | 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. |
| Keywords: | Randomized algorithms Parameter-dependent linear matrix inequalities Computational complexity Conservatism Curse of dimensionality Linear parameter-varying systems |
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