ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability...

In control theory, a control-Lyapunov function (CLF) is an extension of the idea of Lyapunov function V ( x ) {\displaystyle V(x)} to systems with control...

stability (ISS) applies Lyapunov notions to systems with inputs. Lyapunov stability is named after Aleksandr Mikhailovich Lyapunov, a Russian mathematician...

Lyapunov equation Lyapunov exponent Lyapunov fractal Lyapunov function Lyapunov stability Lyapunov time Lyapunov's central limit theorem Lyapunov's condition...

ISS-Lyapunov functions. A smooth function V : R n → R + {\displaystyle V:\mathbb {R} ^{n}\to \mathbb {R} _{+}} is called an ISS-Lyapunov function for...

Lyapunov function is a function of the system f = f(x) whose existence in a system demonstrates stability. It is often useful to imagine a Lyapunov function...

following are named: Lyapunov dimension Lyapunov equation Lyapunov exponent Lyapunov function Lyapunov fractal Lyapunov stability Lyapunov's central limit theorem...

using techniques and theorems named for Aleksandr Lyapunov. In these cases, one defines a function V : R n → R {\displaystyle V:\mathbb {R} ^{n}\rightarrow...

involving eigenvalues of matrices. A more general method involves Lyapunov functions. In practice, any one of a number of different stability criteria...

{\displaystyle u_{x}(\mathbf {0} )=0} . It is also assumed that a Lyapunov function V x {\displaystyle V_{x}} for this stable subsystem is known. That...

optimization refers to the use of a Lyapunov function to optimally control a dynamical system. Lyapunov functions are used extensively in control theory...

The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical...

then the global asymptotic stability of the origin is a consequence of Lyapunov's second theorem. The invariance principle gives a criterion for asymptotic...

decomposition is characterized by a function known as complete Lyapunov function. Unlike traditional Lyapunov functions that are used to assert the stability...

the rate of growth of these moments is limited by the Lyapunov condition given below. Lyapunov CLT—Suppose { X 1 , … , X n , … } {\textstyle \{X_{1},\ldots...

online closed-loop approximate optimal control, the value function is also a Lyapunov function that establishes global asymptotic stability of the closed-loop...

shown to exhibit stable behavior given a suitable Lyapunov control function by Aleksandr Lyapunov in 1892. Thermodynamic systems were treated as early...

In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation...

mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...

In mathematics, Lyapunov fractals (also known as Markus–Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in...

identified as the minimum of a smooth, well-defined potential function (Lyapunov function). Small changes in certain parameters of a nonlinear system can...

in Hamiltonian systems Examination of dissipative quantities (see Lyapunov function) analogous to conserved quantities Linearization via Taylor expansion...

geometry, a synonym for dimension function; in control theory and dynamical systems, a synonym for Lyapunov candidate function; in gauge theory, a synonym for...

generalization of Lyapunov function to input/state/output systems. The construction of the storage function, as the analogue of a Lyapunov function is called...

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in...

come entirely from this space, the Lyapunov function candidate V ( σ ) {\displaystyle V(\sigma )} is a Lyapunov function and x {\displaystyle \mathbf {x}...

equilibrium. Close to equilibrium, one can show the existence of a Lyapunov function which ensures that the entropy tends to a stable maximum. Fluctuations...

minimum in the energy function (which is considered to be a Lyapunov function). Thus, if a state is a local minimum in the energy function it is a stable state...

Lyapunov theorem may refer to: Lyapunov theory, a theorem related to the stability of solutions of differential equations near a point of equilibrium...

performance and robustness. Single Quadratic Lyapunov Function (SQLF) Parameter Dependent Quadratic Lyapunov Function (PDQLF) to bound the achievable level of...