Controllability and Observability of Linear Systems

  • Andrea BacciottiEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 185)


In this chapter we deal with the so-called structural properties of a linear system with input and output. These properties depend only on the coefficients of the mathematical model. We study in particular controllability (which provides a measure of our ability to control the system) and observability (which provides a measure of our ability of extracting information about the state of the system). We obtain algebraic characterizations of these properties. We also study canonical forms i.e., linear transformations of the state space which allow us to rewrite the model. This makes more evident, in this way, recognizing the controllability and observability properties.


Unobservable Space Reduced Order System Minimum Time Problem Controllability Matrix Local Reachability 
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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche “G.L. Lagrange” (DISMA: Dipartimento di eccellenza 2018–22)Politecnico di TorinoTurinItaly

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