Optimality: Minimum-Time for Linear Systems

  • Eduardo D. Sontag
Part of the Texts in Applied Mathematics book series (TAM, volume 6)


We consider time-invariant continuous-time linear systems
with the control-value set U being a compact convex subset of ℝ m . As usual, a control is a measurable map ω: [0,T] → ℝ m so that ω(t) ∈ U for almost all t ∈ [0,T]. We denote by L m (0,T) the set consisting of measurable essentially bounded maps from [0,T] into ℝ m (when m = 1, just L (0,T)) and view the set of all controls as a subset L U (0,T) ⊆ L m (0,T). In this chapter, we write simply L U instead of L U , because, U being compact, all maps into U are essentially bounded.


Maximum Principle Nonzero Vector Supporting Hyperplane Matrix Pair Minimal Time Function 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Eduardo D. Sontag
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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