New exponential stability criteria for neutral system with time-varying delay and nonlinear perturbations

Yuechao Ma, Lihong Zhu
2014 Advances in Difference Equations  
In this paper, the problem of exponential stability for neutral system with time-varying delay and nonlinear perturbations is investigated. By using the technology of model transformations, based on a linear matrix inequality (LMI) and a generalized Lyapunov-Krasovskii function, a new criterion for exponential stability with delay dependence is obtained. Due to a new integral inequality, the result is less conservative. Finally, some numerical examples are presented to illustrate the
more » ... ss of the method. Remark  When G  = G  = G  = G  = , system () is reduced to the traditional neutral system with time delay. However, for the class of neutral systems one has achieved some results in [, ] and the references therein. Remark  When G  =  and G  = G  = G  = I, system () is converted into the system in Ali []. However, our system has more the nature of universality. Remark  When C =  and G  = , system () reduces to the traditional power system with nonlinear perturbations (). However, for the general power system with nonlinear perturbations one has achieved some results in [, -, , ]. We have () Corollary  For prescribed scalar d  > , system () is exponentially admissible with convergence rate ε, if there exist positive-definite matrices P = P   P  P  and positive-definite symmetric matrices Q  , Q  , Q  , W = W  W  * W  and a real matrix Z = Z  Z  * Z  satisfying the following LMI:
doi:10.1186/1687-1847-2014-44 fatcat:tu3diakw2jax3ljyag52ddfjem