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...

ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory...

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

linear for purposes of control design: Feedback linearization And Lyapunov based methods: Lyapunov redesign Control-Lyapunov function Nonlinear damping Backstepping...

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

developed called Rapid Exponentially Stabilizing Control Lyapunov Functions(RES-CLF). Control Lyapunov function are used to stabilize a nonlinear system to...

as a control, external input, stimulus, disturbance, or forcing function. It has been shown that near to a point of equilibrium which is Lyapunov stable...

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

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

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...

assumed that a Lyapunov function V x {\displaystyle V_{x}} for this stable subsystem is known. Backstepping provides a way to extend the controlled stability...

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

mechanician and physicist Lyapunov equation, used in many branches of control theory, such as stability analysis and optimal control Lyapunov fractal, bifurcational...

other continuous control designs. The following theorems form the foundation of variable structure control. Consider a Lyapunov function candidate where...

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}...

time derivative of the system's Lyapunov function is negative definite at that point. In other words, even if the control input is arbitrarily small, a...

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

and state-space methods, widely used within the control systems community. ISS unified the Lyapunov and input-output stability theories and revolutionized...

Krener's theorem Least squares Lyapunov stability Minor loop feedback Perceptual control theory State observer Vector control Labview Matlab Simulink Embedded...

In nonlinear control, the technique of Lyapunov redesign refers to the design where a stabilizing state feedback controller can be constructed with knowledge...

differentiable control-Lyapunov function if and only if it admits a regular stabilizing feedback u(x), that is a locally Lipschitz function on Rn\{0}. The...

Lyapunov–Schmidt reduction or Lyapunov–Schmidt construction is used to study solutions to nonlinear equations in the case when the implicit function theorem...

analogue of Lyapunov's theorem. Bochner measurable function Bochner integral – generalization of the Lebesgue integral to Banach-space valued functionsPages...

dynamics of proteins under the effect of optical tweezers. Lyapunov function — a function whose existence guarantees stability Mohammadi, A.; Spong, Mark...

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

across a variety of areas, including control theory (in particular, for searching for polynomial Lyapunov functions for dynamical systems described by polynomial...

Zinober, Alan S.I., ed. (1994). Variable Structure and Lyapunov Control. Lecture Notes in Control and Information Sciences. Vol. 193. London: Springer-Verlag...

Haddad, W.M.; Chellaboina, VS (2008). Nonlinear Dynamical Systems and Control, a Lyapunov-based approach. Princeton University Press. ISBN 9780691133294. Teschl...

systems as Lyapunov stability, uniform asymptotic stability etc. Let C ( X , Y ) {\displaystyle C(X,Y)} be a space of continuous functions acting from...