Stability theory | Dynamical systems

Marginal stability

In the theory of dynamical systems and control theory, a linear time-invariant system is marginally stable if it is neither asymptotically stable nor unstable. Roughly speaking, a system is stable if it always returns to and stays near a particular state (called the steady state), and is unstable if it goes farther and farther away from any state, without being bounded. A marginal system, sometimes referred to as having neutral stability, is between these two types: when displaced, it does not return to near a common steady state, nor does it go away from where it started without limit. Marginal stability, like instability, is a feature that control theory seeks to avoid; we wish that, when perturbed by some external force, a system will return to a desired state. This necessitates the use of appropriately designed control algorithms. In econometrics, the presence of a unit root in observed time series, rendering them marginally stable, can lead to invalid regression results regarding effects of the independent variables upon a dependent variable, unless appropriate techniques are used to convert the system to a stable system. (Wikipedia).

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Steady state | Lyapunov stability | If and only if | Exponential stability | Regression analysis | Linear time-invariant system | BIBO stability | Complex plane | Random walk | Control theory | Homogeneous differential equation | Dirac delta function | Markov chain | Time-invariant system | Spectral radius | Jordan normal form | Linear system | Time series | Unit root | Econometrics