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...

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

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...

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

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

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...

{\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...

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

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

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...

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

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

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

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

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

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

design is underpinned by a Lyapunov stability analysis that utilizes an auxiliary function, often referred to as the P-function, to establish both asymptotic...

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

Soviet cybernetics, Lyapunov was member of the Academy of Sciences of the Soviet Union and a specialist in the fields of real function theory, mathematical...

named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system. The lemma appears in...

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

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

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

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