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Robust stability and performance anlysis with real parametric and dynamic uncertainties can be naturally formuated as a structured sinular valu(orj problem,where the bloc structured unertainty de thon is algoW to contain both reel and complex blocks

Computational complexity of μ calculation

Automatic Control, IEEE Transactions  , no. 5 (1994): 1000-1002

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摘要

The structured singular value μ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In partic...更多

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  • Robust stability and performance anlysis with real parametric and dynamic uncertainties can be naturally formuated as a structured sinular valu(orj problem,where the bloc structured unertainty de thon is algoW to contain both reel and complex blocks
  • It iass that the reader is familar with this type of robustne analyse, as space constraints preclude c this her For a collection of papers desseceri[b3i]ngantdhetheenrgenrenecigmcooattaiinod and the within.
重点内容
  • Robust stability and performance anlysis with real parametric and dynamic uncertainties can be naturally formuated as a structured sinular valu(orj problem,where the bloc structured unertainty de thon is algoW to contain both reel and complex blocks
  • It iass that the reader is familar with this type of robustne analyse, as space constraints preclude c this her For a collection of papers desseceri[b3i]ngantdhetheenrgenrenecigmcooattaiinod and the within
  • We show that thisir ti problem is NP-had, ie. at leas - had - the NP-complete
  • It is important to note computed m polynomial th being NP-complee is a property of the poblem itelf, not of any particular aith The fact that the mi p problem is NP-hard strongly est, any algorithm to compute p, there will be probl for which the algo rithm cannot find The terminolo theoaf cnompuinttpoiloyanomcoimapllteixmiet.y theory is used extensively in this pap
  • First we show that indefinite quadratic programmingt can be cast as a p problem of "roughly" the same siz
结论
  • TheTmain resls srongly xugges that it is futile to p e xct mh e aulatm#gojmal systems with pue real or mixed poaellxytawl tha a ei p m In pa real l, one s d not at

    Tniznda w kh that p eacty hs results do not mean, artlnwoet e Practical algthms for other

    NP-hard - exis _, b y ~ .

    hranch-and-hwxmin, .eor local e hf5, stonlysggest that a ammiatadtee rets fYoungeta techniques whic taes iInItIo account the structure of which aoximatesp the p c polynomial

    In poblem cal time for typical yield an algonthm problems.

    The anthors thank Profeor John Tsitsikiis at MIT for his comments.

    RePerences [1]J.
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