**Module overview.**
*Stability is the base requirement for the design of a
control system. This module gives a first insight into the design
of closed-loop systems and the problem of their stability. It is
shown by definitions what stability means. Then the most important
stability criteria using the characteristic polynomial (Hurwitz, Routh) are
introduced. Most emphasis is put on the Nyquist criterion, which
can be used with Nyquist and Bode diagrams to design stable
closed-loop systems with given stability margins. To simplify the
stability test in the frequency domain with Nyquist or Bode
diagrams several rules are given. All terms, techniques and rules
are illustrated by examples. *

**Module objectives.**
*When you have completed this module you should be able
to:*

- Understand the stability of linear dynamical systems.
- Understand the algebraic stability criteria for linear systems.
- Know how to test the stability of linear systems described by transfer functions.
- Know how to test the stability of linear systems described by frequency-response characteristics.
- Know how to test the stability of a closed loop from open-loop data.

- Stable and unstable systems
- Definition of stability and stability conditions
- Algebraic stability criteria