Interval stability/stabilization for linear stochastic switched systems with time-varying delay

Highlights：

• Compared with current literature, interval stability control is applied to the stochastic linear time-varying delay systems for the first time. By the definition of interval stability, a criterion for the asymptotic interval stability of the stochastic linear time-varying delay systems is offered. It can determine whether the eigenvalues of the state matrix are in an interval, so as to determine whether the system is stable, and has some dynamic performance.

• By constraining the range of eigenvalues of state matrices, the problem of interval stabilization of the stochastic linear time-varying delay systems is settled, which guarantees the stability of the resulting system and can also control the convergence rate of its state more precisely. Furthermore, a simulation example of the water quality preservation system is used to report the availability of the method.