Abstract:For a class of stochastic differential systems with finite time, the finite time stability and controller design of stochastic linear time-varying systems are studied. First, the definition of finite-time stability is introduced. Based on this definition, a new method for finite-time stability where the assumed Lyapunov function satisfies piecewise continuity and may be discontinuous at each piecewise point is proposed. With the help of the idea of switching systems, the finite time stability of stochastic time-varying systems is studied. Then, based on the finite time stability of the stochastic time-varying system, the controller setting problem of the stochastic time-varying system with feedback controller is considered, and the system controller setting method is given by adopting the step-by-step control method. Finally, based on the linear matrix inequality, a class of linear stochastic time-varying system′s finite time stable controller algorithm is designed, so that the setting of the controller can be effectively realized.