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Stability theory

Stability theory

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Nonlinear and Adaptive Control Systems — Recommend this title to your library

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For control systems, design, one important objective is to ensure the stability of the closed-loop system. For a linear system, the stability can be evaluated in time domain or frequency domain, by checking the eigenvalues of the system matrix or the poles of the transfer function. For nonlinear systems, the dynamics of the system cannot be described by equations in linear state space or transfer functions in general. We need more general definitions about the stability of nonlinear systems. In this chapter, we will introduce basic concepts of stability theorems based on Lyapunov functions.

Chapter Contents:

  • 4.1 Basic definitions
  • 4.2 Linearisation and local stability
  • 4.3 Lyapunov's direct method
  • 4.4 Lyapunov analysis of linear time-invariant systems

Inspec keywords: transfer functions; stability; state-space methods; poles and zeros; closed loop systems; nonlinear control systems; frequency-domain analysis; control system synthesis; Lyapunov methods; matrix algebra; time-domain analysis; eigenvalues and eigenfunctions; linear systems

Other keywords: eigenvalue; control system design; system matrix; stability theory; frequency domain evaluation; linear state space; Lyapunov function; closed-loop system; nonlinear system; time domain evaluation; stability theorem; transfer function poles; system dynamics

Subjects: Nonlinear control systems; Stability in control theory; Control system analysis and synthesis methods; Mathematical analysis; Algebra

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