Stability of unforced linear systems

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.