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  2. Numerical stability - Wikipedia

    en.wikipedia.org/wiki/Numerical_stability

    Von Neumann stability analysis is a commonly used procedure for the stability analysis of finite difference schemes as applied to linear partial differential equations. These results do not hold for nonlinear PDEs, where a general, consistent definition of stability is complicated by many properties absent in linear equations.

  3. Metzler matrix - Wikipedia

    en.wikipedia.org/wiki/Metzler_matrix

    The exponential of a Metzler (or quasipositive) matrix is a nonnegative matrix because of the corresponding property for the exponential of a nonnegative matrix. This is natural, once one observes that the generator matrices of continuous-time Markov chains are always Metzler matrices, and that probability distributions are always non-negative.

  4. Structural stability - Wikipedia

    en.wikipedia.org/wiki/Structural_stability

    In particular, structurally stable vector fields in two dimensions cannot have homoclinic trajectories, which enormously complicate the dynamics, as discovered by Henri Poincaré. Structural stability of non-singular smooth vector fields on the torus can be investigated using the theory developed by Poincaré and Arnaud Denjoy.

  5. Stable polynomial - Wikipedia

    en.wikipedia.org/wiki/Stable_polynomial

    A linear system is BIBO stable if its characteristic polynomial is stable. The denominator is required to be Hurwitz stable if the system is in continuous-time and Schur stable if it is in discrete-time. In practice, stability is determined by applying any one of several stability criteria.

  6. Lyapunov stability - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_stability

    More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis). The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge.

  7. Bistritz stability criterion - Wikipedia

    en.wikipedia.org/wiki/Bistritz_stability_criterion

    [1] [2] The Bistritz test is the discrete equivalent of Routh criterion used to test stability of continuous LTI systems. This title was introduced soon after its presentation. [3] It has been also recognized to be more efficient than previously available stability tests for discrete systems like the Schur–Cohn and the Jury test. [4]

  8. Stability theory - Wikipedia

    en.wikipedia.org/wiki/Stability_theory

    In the former case, the orbit is called stable; in the latter case, it is called asymptotically stable and the given orbit is said to be attracting. An equilibrium solution f e {\displaystyle f_{e}} to an autonomous system of first order ordinary differential equations is called:

  9. Stability radius - Wikipedia

    en.wikipedia.org/wiki/Stability_radius

    The stability radius of a continuous function f (in a functional space F) with respect to an open stability domain D is the distance between f and the set of unstable functions (with respect to D). We say that a function is stable with respect to D if its spectrum is in D. Here, the notion of spectrum is defined on a case-by-case basis, as ...