This paper investigates the leader-following consensus problem of multi-agent systems where the leader is static and the controlling effect of each follower depends on its own state. The control protocols are proposed for two cases: i) for network with switching topologies and undirected information flow; ii) for network with directed information flow and communication time-delays. With the aid of several tools from algebraic graph, matrix theory and stability theory, the sufficient conditions guaranteeing leader-following consensus are obtained by constructing appropriate Lyapunov functions. Simulations are presented to demonstrate the effectiveness of our theoretical results.
Chaos synchronization of systems with perturbations was investigated.A generic nonlinear control scheme to realize chaos synchronization of systems was proposed.This control scheme is flexible and practicable,and gives more freedom in designing controllers in order to achieve some desired performance.With the aid of Lyapunov stability theorem and partial stability theory,two cases were presented:1) Chaos synchronization of the system without perturbation or with vanishing perturbations;2) The boundness of the error state for the system with nonvanishing perturbations satisfying some conditions.Finally,several simulations for Lorenz system were provided to verify the effectiveness and feasibility of our method.Compared numerically with the existing results of linear feedback control scheme,the results are sharper than the existing ones.
The cluster synchronization problem of complex dynamical networks with each node being a Lurie system with external disturbances and time-varying delay is investigated in this paper. Some criteria for cluster synchronization with desired H∞performance are presented by using a local linear control scheme. Firstly, sufficient conditions are established to realize cluster synchronization of the Lurie dynamical networks without time delay. Then, the notion of the cluster synchronized region is introduced, and some conditions guaranteeing the cluster synchronized region and unbounded cluster synchronized region are derived. Furthermore, the cluster synchronization and cluster synchronized region in the Lurie dynamical networks with time-varying delay are considered. Numerical examples are finally provided to verify and illustrate the theoretical results.
In this paper, permanent magnet synchronous motors(PMSMs) are investigated. According to the feature of PMSMs, a novel state equation of PMSMs is obtained by choosing suitable state variables. Based on the state equation, robust controllers are designed via interval matrix and PI control idea.In terms of bilinear matrix inequations, sufficient conditions for the existence of the robust controller are derived. In order to reduce the conservation and the dependence on parameter,the control inputs of PMSMs are divided into two parts, a feedforward control input and a feedback control input, and relevant sufficient conditions for the existence of the controller are obtained. Because of the suitable choice of state variables, the proposed control strategies can cope with the load uncertainty and have robustness for disturbance. Finally, simulations are carried out via Matlab/Simulink soft to verify the effectiveness of the proposed control strategies. The performance of the proposed control strategies are demonstrated by the simulation results.
