Abstract
In modern science technology and many motion process of engineering fields, such as neural network activity, movement of missile and spacecraft, control of robot and so on, there are many phenomena which are suddenly changed when their movement is disturbed in some time. The mathematical model of the instantaneous phenomena which we referred is impulsive differential equation. More and more control experts and mathematicians pay close attention to impulsive system, because the study of impulsive has the wide actual background and the value of the application. The robust control problems of the uncertain linear impulsive delay system are studied. Based on the stability of the impulsive delay system, we take advantage of the stability theory of Lyapunov, Lyapunov function and the technology of linear matrix inequality to design a robust feedback controller in order to eliminate the impact of pulse and time delay on the stability of the system. The controller can be got by the way of solving linear matrix inequality by using MATLAB toolbox. And some sufficient conditions of the robust exponential stability are proposed so that the system contains robust feedback control.
Highlights
The robust problem is a widespread problem in the control system
Using synchronous error feedback approach constructors the suitable Lyapunov function for the synchronous analysis of the chaotic systems to give out a sufficient condition for a class of delay chaotic system pulse synchronous exponential stability (Chen and Xu, 2012; Cheng et al, 2012; Yang and Xu, 2007a)
The robust stability of the Hopfield impulsive neural networks was studied based on Lyapunov functions to get the sufficient conditions of the robust stability and robust asymptotic stability of the pulse Hopfield neural network, on the basis, design the implement pulse controller to calm Hopfield neural network
Summary
The robust problem is a widespread problem in the control system. In the control system, the feedback control is the most basic control (Guan et al, 2001; Stamova and Stamov, 2001). Using synchronous error feedback approach constructors the suitable Lyapunov function for the synchronous analysis of the chaotic systems to give out a sufficient condition for a class of delay chaotic system pulse synchronous exponential stability (Chen and Xu, 2012; Cheng et al, 2012; Yang and Xu, 2007a). This study is mainly based on the stability theory of Lyapunov to select appropriate Lyaounov function combined with linear matrix inequalities and design the control system of the robust feedback control in order to eliminate the impact of the time delay and the pulse of the system, which makes the system to achieve robust exponential stability
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