The main contributions of this paper are twofold: (1) the concept of finite-time stability for polynomial fuzzy model is firstly proposed, and (2) finite-time stabilizing controller is designed to stabilize the nonlinear system
represented in the form of SOS, which is superior to the form of LMIs.
Fu, "Three-stage unscented Kalman filter for state and fault estimation of nonlinear system
with unknown input," Journal of The Franklin Institute, vol.
In particular, it has been shown that a TS dynamic model obtained through the nonlinear sector transformation approach can describe the overall behavior of a highly complex nonlinear system
with a high degree of accuracy [11, 14].
SDRE is a nonlinear system
control method proposed in the 90s of last century.
With the developing of nonlinear system
theories, expanding the scope of delayed systems to nonlinear systems
has aroused great interests.
In order to demonstrate the position control enhancement for the nonlinear system
, the proposed controller is compared with classical PID controller using simulation results with and without external disturbance.
The Takagi-Sugeno (T-S) fuzzy model is a type of fuzzy models which is able to give a local linear representation of the nonlinear system
. Such a model is able to approximate a wide class of nonlinear systems
because they are considered powerful in modelling and control of complex dynamic systems.
For nonlinear systems
, the early presented EKF  can do nothing for the complex nonlinear systems
, especially when the nonlinear system
cannot be linearized by Taylor's expansion .
In the past decade, control and synchronization of nonlinear system
in industry have attracted much attention.
Because dropping shock is one of the main factors that cause the mechanical damage of most packaged products potentially in the transportation, the numerical results of a nonlinear cushioning system were derived by applying Runge-Kutta method and the dropping damage boundary concept of the packaged article was proposed , but no research has been conducted on whether the drop equivalent test is still suitable for nonlinear system
. Then, some researchers improved the accuracy of a nonlinear system
drop test [7,8].
Now we select the state space variables as x = h and u = [q.sub.v] and we obtain the nonlinear system
In general, the goal of the MMP is to compensate a given nonlinear system
in order to make its behaviour similar to that of a given nonlinear model.