that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if...

astronomer Mikhail Lyapunov and the brother of the pianist and composer Sergei Lyapunov. Lyapunov is known for his development of the stability theory of a dynamical...

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

stability and a domain of attraction from dynamical system theory. Researchers applying mathematical models from system dynamics usually use Lyapunov...

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

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

values A and B. A Lyapunov fractal is constructed by mapping the regions of stability and chaotic behaviour (measured using the Lyapunov exponent λ {\displaystyle...

A-stability. They are related to some concept of stability in the dynamical systems sense, often Lyapunov stability. It is important to use a stable method when...

matrices. A more general method involves Lyapunov functions. In practice, any one of a number of different stability criteria are applied. Many parts of the...

is important for the problem of the stability of the Solar System. However, empirical estimation of the Lyapunov time is often associated with computational...

plane method Lyapunov stability analysis Singular perturbation method The Popov criterion and the circle criterion for absolute stability Center manifold...

Asymptotic stability Exponential stability Linear stability Lyapunov stability Marginal stability Orbital stability Structural stability Stability (probability)...

bounded input. Stability for nonlinear systems that take an input is input-to-state stability (ISS), which combines Lyapunov stability and a notion similar...

Lyapunov function is used to test whether a dynamical system is (Lyapunov) stable or (more restrictively) asymptotically stable. Lyapunov stability means...

their periods). Unlike Lyapunov stability, which considers perturbations of initial conditions for a fixed system, structural stability deals with perturbations...

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

used within the control systems community. ISS unified the Lyapunov and input-output stability theories and revolutionized our view on stabilization of...

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...

Asymptotic stability Linearization (stability analysis) Lyapunov stability Orbital stability Stability theory Vakhitov–Kolokolov stability criterion V...

the fact that positive recurrent Markov chains exhibit a notion of "Lyapunov stability" in terms of returning to any state while starting from it within...

to modify estimates in real-time (i.e., as the system operates). Lyapunov stability is used to derive these update laws and show convergence criteria...

processes are those that possess null recurrent classes. Lyapunov stability Exponential stability Gene F. Franklin; J. David Powell; Abbas Emami-Naeini (2006)...

definitions through which it may be assessed: BIBO stability Linear stability Lyapunov stability Orbital stability This set index article includes a list of related...

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...

In mathematics, the Lyapunov–Schmidt reduction or Lyapunov–Schmidt construction is used to study solutions to nonlinear equations in the case when the...

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

relative graph of a nonlinear operator. Additionally, other stability criteria like Lyapunov methods can also be applied for non-linear systems. Although...

systems is by studying the stability of the system far from equilibrium. Close to equilibrium, one can show the existence of a Lyapunov function which ensures...

notions of stability have been introduced in the study of dynamical systems, such as Lyapunov stability or structural stability. The stability of the dynamical...