ON THE ROLE OF MATRIX-WEIGHTS ELEMENTS IN CONSENSUS ALGORITHMS FOR MULTI-AGENT SYSTEMS

This paper extends the concept of weighted graphs to matrix weighted graphs. The consensus algorithms dictate that all agents reach consensus when the weighted graph is connected. However, it is not always the case for matrix weighted graphs. The conditions leading to different types of consensus have been extensively analysed based on the properties of matrix-weighted Laplacians and graph theoretic methods. However, in practice, there is concern on how to pick matrix-weights to achieve some desired consensus, or how the change of elements in matrix weights affects the consensus algorithm. By selecting the elements in the matrix weights, different clusters may be possible. In this paper, we map the roles of the elements of the matrix weights in the systems consensus algorithm. We explore the choice of matrix weights to achieve different types of consensus and clustering. Our results are demonstrated on a network of three agents where each agent has three states.

On the real, rational, bounded, unit interpolation problem in ℋ∞ and its applications to strong stabilization

One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in [Formula: see text] satisfying certain interpolation conditions. The problem is transformed into a classical Nevanlinna–Pick interpolation problem by using a predetermined structure for the unit interpolating function and analysed through the associated Pick matrix. Sufficient conditions for the existence of the bounded unit interpolating function are derived. Based on these conditions, an algorithm is proposed to compute the unit interpolating function through an optimal solution to the Nevanlinna–Pick problem. The conservatism caused by the sufficient conditions is illustrated through strong stabilization examples taken from the literature.