Interval stability and interval stabilization of linear stochastic systems with time‐varying delay
Huasheng Zhang, Jianwei Xia, Ju H. Park, Wei Sun, Guangming Zhuang
Abstract
Abstract This article first investigates the criterion of interval stability for linear stochastic systems with time‐varying delay via equivalent systems and Lyapunov–Krasovskii (L‐K) functionals. Different from existing stability conditions, the criterion of interval stability can be used to make a more accurate judgment of the stability for linear time‐delay systems. In other words, the new criterion can judge not only the stability of the system but also the speed of its convergence. Meanwhile, based on the criterion of the interval stability, the condition of interval stabilization is derived, which cannot only ensure the stability of the linear time‐delay systems, but also adjust the convergence rate of the states to the ideal level. A numerical instance is presented to illustrate the advantages of the resulting interval stabilization criterion.