Decentralized Resilient Finite-Time Control Using Partial Variables of Fractional-Order Interconnected Delayed Systems Under Stochastic Disturbances

This article focuses on problems of stability and control of fractional-order interconnected delayed systems (FOIDSs) subject to stochastic disturbances. First, dynamical model for the FOIDSs under the stochastic disturbances is constructed. Simultaneously, a decentralized resilient finite-time control technique based on partial variables of the FOIDSs is put forward. This technique can not only make the system achieve stability within a limited time but also thrift the control cost and enhance the control flexibility. Second, some new lemmas are introduced, combining fractional calculus and Lyapunov function method, stability research of the FOIDSs is presented. In the meantime, novel stability results are developed. Range of the order $\alpha$ for the FOIDSs is further expanded. In addition, the obtained results are applicable not only to general FOIDSs but also to some real systems, for instance, interconnected power systems. Ultimately, the validity of the derived criteria is illustrated through a couple of numerical examples, and strengths of the proposed control approach are shown by means of comparison.