Stabilization of systems with interval time-varying delay based on delay decomposing approach

摘要

Abstract The paper considers the stabilization for systems with interval time-varying delay. By decomposing the delay interval into multiple equidistant subintervals and considering the triple integral terms, a novel Lyapunov-krasovskii functional(LKF) is defined. Then extended integral inequality and convex combination approach are used to estimate the derivative of the constructed functional, and as a result, the new stability criterion with less conservatism and decision variables is obtained. On this basis, the state feedback controller is designed, by using linearization method, the existence condition of controller is obtained in terms of linear matrix inequalities(LMIs), and the specific form of controller is also given, moreover, by selecting the appropriate parameter value, the stabilization time of the system can be reduced. Numerical examples are given to illustrate the effectiveness of the proposed method. Highlights ? When using delay decomposing method, the decision variables number becomes more when the delay subintervals number becomes larger, which lead to the complexity and the computational burden of the main result. In this paper, this shortcoming is avoided, the computational burden does not increase. ? In order to reduce the conservatism of the main result, a novel LKF is constructed, which involves the triple integral term augment term for each delay subinterval, so that more information of the time delay is employed, and then the extended integral inequality and convex combination method are used to estimate the derivative of the constructed functional, all of which lead to the less conservative result. ? Through using some inequalities and the extended linearization method, the existence condition of controller is obtained in terms of LMIs, and by selecting the appropriate value of the scalar, the stabilization time of the system can be reduced. ]]>