# Lyapunov function

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## Lyapunov function

[lē′ap·ə‚nȯf ‚fəŋk·shən]
(mathematics)
A function of a vector and of time which is positive-definite and has a negative-definite derivative with respect to time for nonzero vectors, is identically zero for the zero vector, and approaches infinity as the norm of the vector approaches infinity; used in determining the stability of control systems. Also spelled Liapunov function.
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These control structures enable getting a general nonlinear time-variant continuous system into a defined steady state using a prescribed reference model, while the structural complexity of the designed controllers depends on the suitable choice of the Lyapunov function [29]-[32].
Lyapunov function is derived in consideration of the aforementioned queues (Z(t),H(t),Q(t)) as Eqn.
Selecting the Lyapunov function using sliding mode is a natural and reasonable approach to get to the desired control goals that is tracking desired trajectory.
Keywords: Chemical kinetics, Chemical equilibrium, Lyapunov function, Invariant manifolds, Model reduction.
This map was made by varying the output voltage from 4 V to 9 V and inductor current from 0 A to 1 A, calculating a current command from the augmented control law, calculating the Lyapunov function evaluation from the error estimates and ensuring that they were less than a bound (see Eq.
We introduce the following positive Lyapunov function with two gain coefficients as follows [8],[9],[14],[18]
Meanwhile, from the former theorem, with the control of the event-based strategy, the derivative of the Lyapunov function (12) is less than 0 when the consensus is not achieved and is equal to 0 when the consensus is achieved.
Multifunction converter based on Lyapunov function used in a photovoltaic system," Turkish Journal of Electrical Engineering and Computer Science, 22(4): 893-908 (2014).
The result thus obtained is verified by Lyapunov function to verify the paths obtained.
Suppose [eta] = (y, [lambda], [mu]), and then establish Lyapunov function in following form:
The main setback of this method is precisely to find a Lyapunov function, because there is not a systematic method for finding.

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