Exponential stability conditions for switched linear stochastic systems with time-varying delay

The authors investigate the stability in mean-square sense for switched stochastic systems with time-varying delay by using multiple Lyapunov functionals method. In order to characterise the joint effects of switching and time delay on stability, some practical techniques are applied in computing the Lyapunov functional constructed for individual subsystem. The first one among others is to make use of Itô calculus rules to reduce the conservatism produced by noise since it basically plays a negative role for preserving stability. Also, the authors present a necessary number of slack matrices to create convex conditions so as to accommodate the computation to time-varying delay. In the following, the authors show the stability of overall system via confining switching frequency within a certain level. An example is used to illustrate the method with describing the mutually constraint situation of switching and time delay.