Stability of Unforced Linear Systems

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


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.


Classical Lyapunov Theorem Internal Stability Properties Lyapunov Matrix Equation Routh-Hurwitz Criterion Quadratic Lyapunov Function 
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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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