Abstract: In this paper, we consider the control of time delay system
by Proportional-Integral (PI) controller. By Using the Hermite-
Biehler theorem, which is applicable to quasi-polynomials, we seek
a stability region of the controller for first order delay systems. The
essence of this work resides in the extension of this approach to
second order delay system, in the determination of its stability region
and the computation of the PI optimum parameters. We have used
the genetic algorithms to lead the complexity of the optimization
problem.
Abstract: In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. Finally, an example is given to illustrate our results by using MATLAB LMI toolbox.