On the λ-equations for matching control laws

David Auckly, Lev Kapitanski

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely characterized by a linear system of first order partial differential equations for one set of variables (λ) followed by a linear system of first order partial differential equations for the second set of variables (ĝ, V̂). Here we derive a new first order system of partial differential equations that encodes all compatibility conditions for the λ-equations. We give four examples illustrating different features of matching control laws, The last example is a system with two unactuated degrees of freedom that admits only basic solutions to the matching equations. There are systems with many matching control laws where only basic solutions are potentially useful. We introduce a rank condition indicating when this is likely to be the case.

Original languageEnglish (US)
Pages (from-to)1372-1388
Number of pages17
JournalSIAM Journal on Control and Optimization
Issue number5
StatePublished - Oct 13 2003
Externally publishedYes


  • Matching control laws
  • Nonlinear control
  • Stabilization
  • λ-equations

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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