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...
9 KB (1,668 words) - 18:22, 30 May 2024
ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory...
7 KB (1,085 words) - 14:27, 29 July 2024
Lyapunov equation Lyapunov exponent Lyapunov fractal Lyapunov function Lyapunov stability Lyapunov time Lyapunov's central limit theorem Lyapunov's condition...
14 KB (1,585 words) - 02:40, 12 August 2024
linear for purposes of control design: Feedback linearization And Lyapunov based methods: Lyapunov redesign Control-Lyapunov function Nonlinear damping Backstepping...
12 KB (1,328 words) - 20:01, 14 January 2024
The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical...
8 KB (1,500 words) - 12:19, 18 May 2024
developed called Rapid Exponentially Stabilizing Control Lyapunov Functions(RES-CLF). Control Lyapunov function are used to stabilize a nonlinear system to...
13 KB (1,610 words) - 04:53, 16 April 2024
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...
24 KB (3,883 words) - 16:08, 9 July 2024
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...
13 KB (2,370 words) - 08:04, 28 February 2023
online closed-loop approximate optimal control, the value function is also a Lyapunov function that establishes global asymptotic stability of the closed-loop...
10 KB (1,461 words) - 18:14, 31 July 2023
geometry, a synonym for dimension function; in control theory and dynamical systems, a synonym for Lyapunov candidate function; in gauge theory, a synonym for...
453 bytes (90 words) - 10:33, 14 November 2010
generalization of Lyapunov function to input/state/output systems. The construction of the storage function, as the analogue of a Lyapunov function is called...
45 KB (6,461 words) - 20:40, 7 June 2024
Backstepping (redirect from Backstepping control)
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...
41 KB (9,136 words) - 15:11, 22 February 2024
In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation...
26 KB (3,187 words) - 03:52, 22 July 2024
mechanician and physicist Lyapunov equation, used in many branches of control theory, such as stability analysis and optimal control Lyapunov fractal, bifurcational...
1 KB (203 words) - 00:57, 19 July 2021
other continuous control designs. The following theorems form the foundation of variable structure control. Consider a Lyapunov function candidate where...
52 KB (8,248 words) - 00:27, 29 December 2023
Central limit theorem (redirect from Lyapunov's central limit theorem)
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}...
65 KB (8,861 words) - 09:16, 20 August 2024
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...
817 bytes (120 words) - 22:22, 15 February 2022
performance and robustness. Single Quadratic Lyapunov Function (SQLF) Parameter Dependent Quadratic Lyapunov Function (PDQLF) to bound the achievable level of...
9 KB (1,234 words) - 17:39, 18 June 2024
Input-to-state stability (category Nonlinear control)
and state-space methods, widely used within the control systems community. ISS unified the Lyapunov and input-output stability theories and revolutionized...
22 KB (3,536 words) - 18:42, 23 July 2024
Krener's theorem Least squares Lyapunov stability Minor loop feedback Perceptual control theory State observer Vector control Labview Matlab Simulink Embedded...
5 KB (382 words) - 12:07, 30 October 2023
In nonlinear control, the technique of Lyapunov redesign refers to the design where a stabilizing state feedback controller can be constructed with knowledge...
1 KB (212 words) - 02:17, 24 January 2020
Artstein's theorem (category Control theory)
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...
2 KB (195 words) - 07:33, 17 April 2023
Lyapunov–Schmidt reduction or Lyapunov–Schmidt construction is used to study solutions to nonlinear equations in the case when the implicit function theorem...
6 KB (968 words) - 00:19, 22 May 2021
Vector measure (redirect from Lyapunov's theorem)
analogue of Lyapunov's theorem. Bochner measurable function Bochner integral – generalization of the Lebesgue integral to Banach-space valued functionsPages...
12 KB (1,519 words) - 23:02, 10 March 2024
Chetaev instability theorem (redirect from Chetaev function)
dynamics of proteins under the effect of optical tweezers. Lyapunov function — a function whose existence guarantees stability Mohammadi, A.; Spong, Mark...
2 KB (246 words) - 21:06, 12 June 2024
Systems thinking (section Feedback control systems)
shown to exhibit stable behavior given a suitable Lyapunov control function by Aleksandr Lyapunov in 1892. Thermodynamic systems were treated as early...
19 KB (1,943 words) - 16:52, 31 May 2024
across a variety of areas, including control theory (in particular, for searching for polynomial Lyapunov functions for dynamical systems described by polynomial...
16 KB (2,685 words) - 13:09, 11 June 2024
Zinober, Alan S.I., ed. (1994). Variable Structure and Lyapunov Control. Lecture Notes in Control and Information Sciences. Vol. 193. London: Springer-Verlag...
5 KB (485 words) - 21:44, 12 June 2022
Haddad, W.M.; Chellaboina, VS (2008). Nonlinear Dynamical Systems and Control, a Lyapunov-based approach. Princeton University Press. ISBN 9780691133294. Teschl...
10 KB (1,436 words) - 14:43, 23 June 2024
systems as Lyapunov stability, uniform asymptotic stability etc. Let C ( X , Y ) {\displaystyle C(X,Y)} be a space of continuous functions acting from...
3 KB (552 words) - 17:24, 1 April 2024