enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. 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).

  3. 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

  4. Lyapunov stability - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_stability

    This example shows a system where a Lyapunov function can be used to prove Lyapunov stability but cannot show asymptotic stability. Consider the following equation, based on the Van der Pol oscillator equation with the friction term changed:

  5. Input-to-state stability - Wikipedia

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

    It can be easily proved, [13] that if is an iISS-Lyapunov function with , then is actually an ISS-Lyapunov function for a system . This shows in particular, that every ISS system is integral ISS. The converse implication is not true, as the following example shows.

  6. Conley's fundamental theorem of dynamical systems - Wikipedia

    en.wikipedia.org/wiki/Conley's_fundamental...

    Conley's decomposition is characterized by a function known as complete Lyapunov function. Unlike traditional Lyapunov functions that are used to assert the stability of an equilibrium point (or a fixed point) and can be defined only on the basin of attraction of the corresponding attractor, complete Lyapunov functions must be defined on the whole phase-portrait.

  7. Lyapunov optimization - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_optimization

    A Lyapunov function is a nonnegative scalar measure of this multi-dimensional state. Typically, the function is defined to grow large when the system moves towards undesirable states. System stability is achieved by taking control actions that make the Lyapunov function drift in the negative direction towards zero.

  8. Stability theory - Wikipedia

    en.wikipedia.org/wiki/Stability_theory

    4 Lyapunov function for general dynamical systems. ... for example, is a stable partial ... Stability theory addresses the following questions: Will a nearby orbit ...

  9. 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.