In this paper, we study pinning control problem of coupled dynamical systemswith stochastically switching couplings and stochastically selectedcontroller-node set. Here, the coupling matrices and the controller-node setschange with time, induced by a continuous-time Markovian chain. By constructingLyapunov functions, we establish tractable sufficient conditions forexponentially stability of the coupled system. Two scenarios are consideredhere. First, we prove that if each subsystem in the switching system, i.e. withthe fixed coupling, can be stabilized by the fixed pinning controller-node set,and in addition, the Markovian switching is sufficiently slow, then thetime-varying dynamical system is stabilized. Second, in particular, for theproblem of spatial pinning control of network with mobile agents, we concludethat if the system with the average coupling and pinning gains can bestabilized and the switching is sufficiently fast, the time-varying system isstabilized. Two numerical examples are provided to demonstrate the validity ofthese theoretical results, including a switching dynamical system betweenseveral stable sub-systems, and a dynamical system with mobile nodes andspatial pinning control towards the nodes when these nodes are being in apre-designed region.
展开▼
