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
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.
20), the derivative of the Lyapunov function
can be written as
We introduce the following positive Lyapunov function
with two gain coefficients as follows ,,,
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.