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  2. Lyapunov stability - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_stability

    The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs.

  3. Lyapunov function - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_function

    A Lyapunov function for an autonomous dynamical system {: ˙ = ()with an equilibrium point at = is a scalar function: that is continuous, has continuous first derivatives, is strictly positive for , and for which the time derivative ˙ = is non positive (these conditions are required on some region containing the origin).

  4. Input-to-state stability - Wikipedia

    en.wikipedia.org/wiki/Input-to-state_stability

    ISS unified the Lyapunov and input-output stability theories and revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, stability of nonlinear interconnected control systems, nonlinear detectability theory, and supervisory adaptive control. This made ISS the dominating stability paradigm in ...

  5. Lyapunov equation - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_equation

    In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is A X A H − X + Q = 0 {\displaystyle AXA^{H}-X+Q=0} where Q {\displaystyle Q} is a Hermitian matrix and A H {\displaystyle A^{H}} is the conjugate transpose of A {\displaystyle A} , while the continuous-time Lyapunov equation is

  6. Control-Lyapunov function - Wikipedia

    en.wikipedia.org/wiki/Control-Lyapunov_function

    The ordinary Lyapunov function is used to test whether a dynamical system is (Lyapunov) stable or (more restrictively) asymptotically stable. Lyapunov stability means that if the system starts in a state x ≠ 0 {\displaystyle x\neq 0} in some domain D , then the state will remain in D for all time.

  7. Lyapunov optimization - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_optimization

    Lyapunov functions are used extensively in control theory to ensure different forms of system stability. The state of a system at a particular time is often described by a multi-dimensional vector. A Lyapunov function is a nonnegative scalar measure of this multi-dimensional state.

  8. Lyapunov–Malkin theorem - Wikipedia

    en.wikipedia.org/wiki/Lyapunov–Malkin_theorem

    The Lyapunov–Malkin theorem (named for Aleksandr Lyapunov and Ioel Malkin ) is a mathematical theorem detailing stability of nonlinear systems. [ 1 ] [ 2 ] Theorem

  9. Talk:Lyapunov stability - Wikipedia

    en.wikipedia.org/wiki/Talk:Lyapunov_stability

    But the article is, actually, wrong in the following sense: we're dealing with Lyapunov Stability of Equilibrium Points. There's no need to specify if the system is unforced. The concept of Lyapunov Stability is, actually, original from the study of trajectories from ODEs. Then, you should define when a solution of a ODE is Lyapunov Stable.