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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. 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.

4. 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

5. Massera's lemma - Wikipedia

   en.wikipedia.org/wiki/Massera's_lemma

   In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system. [1] The lemma appears in ( Massera 1949 , p. 716) as the first lemma in section 12, and in more general form in ( Massera 1956 , p. 195) as lemma 2.

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

   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.

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   AOL App Ad-Free email 1. Enjoy an ad-free experience across all email accounts in your AOL mobile app. Select your default screen. Customize the experience you see first when you open the AOL app.

9. Input-to-state stability - Wikipedia

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

   In the ISS theory for time-delay systems two different Lyapunov-type sufficient conditions have been proposed: via ISS Lyapunov-Razumikhin functions [17] and by ISS Lyapunov-Krasovskii functionals. [18] For converse Lyapunov theorems for time-delay systems see. [19]