Abstract
In this chapter the study of unforced linear systems is continued. We focus in particular on the stability properties of the equilibrium position (the origin). This corresponds to the study of the internal stability properties of a system with input and output. We state and prove the classical Lyapunov Theorem which allows us to reduce the stability analysis to an algebraic problem (computation of the eigenvalues of a matrix). We also introduce the quadratic Lyapunov functions and the Lyapunov matrix equation. The Routh-Hurwitz criterion is given without proof.
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
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). Stability of Unforced 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-02405-5_3
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)