Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We stress that in general, the construction does not work if the orthogonality requirement is neglected: this is an important difference with respect to the construction of the controllability form. The reason of this fact is implicit in the statement of Theorem 5.6.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Bacciotti, A. (2019). Controllability and Observability of Linear Systems. In: Stability and Control of Linear Systems. Studies in Systems, Decision and Control, vol 185. Springer, Cham. https://doi.org/10.1007/978-3-030-02405-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-02405-5_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-02404-8
Online ISBN: 978-3-030-02405-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)