Controllability and Observability

  • Jan Willem Polderman
  • Jan C. Willems
Part of the Texts in Applied Mathematics book series (TAM, volume 26)


In this chapter we introduce two concepts that play a central role in systems theory. The first concept is controllability; the second is observability. Loosely speaking, we call a behavior controllable if it is possible to switch from one trajectory to the other within the behavior. The advantage is that in a controllable behavior, one can, in principle, always move from an”undesirable” trajectory to a “desirable” one. Observability, on the other hand, is not a property of the behavior as such; rather it is a property related to the partition of the trajectories w into two components w 1 and w 2 . We call w 2 observable from w 1 if w 1 and the laws that governing the system dynamics uniquely determine w 2 . Thus observability implies that all the information about w is already contained in w 1 .


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Jan Willem Polderman
    • 1
  • Jan C. Willems
    • 2
  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands
  2. 2.Mathematics InstituteUniversity of GroningenGroningenThe Netherlands

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