Limit stability
The term cross-stable or marginal stability comes from the stability theory and refers to a system whose output does not rise, but not merging into a stable state. An example of this is a continuous oscillation, the amplitude of which is neither smaller nor larger.
Stability is an important property of systems . Systems can be divided into unstable and stable systems. The eigenvalues of the system matrix A of the state space model , which at the same time also represent the roots of the characteristic polynomial and the poles of the transfer function , are decisive for the classification .
Limit stability is present when a real pole or a complex conjugate pair of poles is on the imaginary axis (i.e. when the real part is equal to zero), while all other poles are in the left complex half-plane. If poles with a real part of zero occur more than once, it is no longer possible to evaluate the stability. Such systems can also be unstable.
A system is stable if all eigenvalues (or roots or poles) have a negative real part and are therefore in the left half-plane of the complex plane ( pole-zero diagram ).
The system is unstable if at least one of these real parts is positive and therefore lies in the right half-plane.
literature
- Otto Föllinger: Nonlinear Regulations 2nd 7th edition, R. Oldenbourg Verlag, Munich Vienna 1993, ISBN 3-486-22503-0 .
- Mark Aronovich Aĭzerman, Feliks Ruvimovich Gantmakher: The absolute stability of control systems. R. Oldenbourg Verlag, Munich 1960.
Web links
- Stability and limit stability (accessed on February 18, 2016)
- Lecture notes Uni Saarland (accessed on February 18, 2016)