Marginal stability

The term cross- border stable or stability comes from the stability theory and refers to a system whose output does not increase, but does not pass into a stable state. One example is a continuous oscillation, whose amplitude is neither smaller nor larger.

Stability is an important feature of systems. Systems can be divided into unstable and stable systems. Crucial for the classification are the eigenvalues ​​of the system matrix A of the state space model, which are the roots of the characteristic polynomial, and the poles of the transfer function at the same time.

Marginal stability occurs when a real pole and a complex conjugate pair of pole on the imaginary axis are, ie when the real part is equal to zero. For multiple such poles occur is an assessment of stability no longer possible. Such systems may be unstable.

A system is stable if all eigenvalues ​​(or roots or poles ) have a negative real part and thus in the left half plane of the complex plane ( pole - zero plot ) lie.

The system is unstable, when at least one of the real part is positive, and thus is located in the right half plane.