Robust Pinning control of heterogeneous complex networks with jointly connected topologies and time-varying parametric uncertainty

The pinning/leader control problems provide the design of the leader or pinning controller in order to guide a complex network to a desired trajectory or target (synchronization or consensus). Let a time invariant complex network, the design includes the tuning of pinning gain and number of nodes to pin. Usually lower is the number of pinned nodes larger is the pinning gain required to assess network synchronization (consensus). On the other side, realistic application scenario of complex networks is characterized by switching topologies, time varying node coupling strength and link weight that make hard to solve the pinning/leader control problem. Additionally, the system dynamics at nodes can be heterogeneous. In this paper we derive robust stabilization conditions of time varying heterogeneous complex networks with jointly connected topologies when coupling strength and link weight interactions are affected by time varying uncertainties. By employing Lyapunov stability theory and Linear Matrix Inequality (LMI) technique, we formulate stabilizability conditions to design a pinning/leader control gain to guarantee the asymptotic network synchronization to the pinner trajectory. The effectiveness of the proposed approach is shown by several design examples applied to a paradigmatic well known complex network composed of heterogeneous Chua’s circuits. The proposed LMIs are low computationally demanding and can be easily solved by the MATLAB toolbox, also for large scale complex networks.