In this paper, the observer-based controller design problem for tracking a constant reference input in Lipschitz nonlinear systems is addressed. To this end, at first, a state feedback controller is proposed and sufficient conditions for solvability of the problem are obtained in terms of linear matrix inequality feasibility conditions. Then, it is shown that for the considered Lipschitz nonlinear system, the separation principle holds and the estimation state variables can be used instead of the state variables. Subsequently, an observer for estimating the states of the system and also an observer-based controller is designed. Simulation results on a flexible link are given to verify the effectiveness of the proposed controller.

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In this paper, the problem of pinning impulsive synchronization for complex dynamical networks with directed or undirected but a strongly connected topology is investigated. To remedy this problem, we propose an efficient algorithm to find certain suitable nodes to be controlled via pinning and these selected nodes, in general, could be different at distinct impulsive time instants. The proposed algorithm guarantees the efficiency of the designed pinning impulsive strategy for the global exponential synchronization of state-coupled dynamical networks under an easily-verified condition. In other words, impulsive controllers and an efficient algorithm are designed to control a small fraction of the nodes, which successfully controls the whole dynamical network. Furthermore, we also estimate the upper bound of the number of pinning nodes, which is shown to be closely related to the impulsive intervals. The relationship implies that the required number of pinning nodes, which should be controlled for the successful control of the whole dynamical network, can be greatly reduced by reducing the impulses interval. Finally, simulations of scale-free and small-world networks are given to illustrate the effectiveness of the theoretical results.

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