Marginal stability
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In the theory of dynamical systems, and control theory, a continuous linear time-invariant system is marginally stable if and only if the real part of every eigenvalue (or pole) in the system's transfer-function is non-positive, and all eigenvalues with zero real value are simple roots (i.e. the eigenvalues on the imaginary axis are all distinct from one another). If all the poles have strictly negative real parts, the system is instead asymptotically stable.
A discrete linear time-invariant system is marginally stable if and only if the transfer function's spectral radius is 1. That is, the greatest magnitude of any of the eigenvalues (or poles) of the transfer function is 1. The values of the poles must also be distinct. If the spectral radius is less than 1, the system is instead asymptotically stable.
[edit] Practical Consequences
A marginally stable system is one that, if given an impulse of finite magnitude as input, will not "blow up" and give an unbounded output. However, oscillations in the output will persist indefinitely, and so there will, in general, be no final steady-state output. If the system is given a step as an input, the system's output will increase indefinitely, with the system effectively acting as an integrator on the input, and so a marginally stable system is not a Bounded Input/Bounded Output system.
