Also Lyapunov function
is necessary for the process of designing adaptive controllers.
The Lyapunov function
will determine the gains of the PI-fuzzy controller to ensure the convergence of the actual speed of the DSIM to its reference value.
Taking time derivative of the Lyapunov function
, (29) can be written as
If one can find a Lyapunov function
V(t, x(t)) as well as three class-K functions [g.sub.i], i = 1, 2, 3 such that
In the first part, the Lyapunov function
will be constructed and the stability of [??] subsystem will be proved.
Akagi, "Modified Model Predictive Control of a Bidirectional AC-DC Converter Based on Lyapunov Function
for Energy Storage Systems," IEEE Transactions on Industrial Electronics, vol.
firstly, we give two results about the existence and uniqueness of the periodic solution of (2) by using the fixed point theory; then, we use Lyapunov function
method and discuss the stability of the periodic solution; further, we discuss (1) and get the existence of the periodic solution of (1); some new results are obtained.
The method generalizes the idea which shows that the system is stable if there are some Lyapunov function
candidates for the system.
In  the authors propose a control law based on backstepping  and Lyapunov function
so as to stabilize the global system.
In recent years, the barrier Lyapunov function
(BLF) state-constrained control method has been paid attention by scholars.
We firstly consider the poultry subsystem in farms and define a Lyapunov function
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.