Passivity and Control for Multiweighted and Directed Fractional-Order Network Systems

We conduct the study of passivity and control for multiweighted and directed fractional-order network systems (MDFONSs) in this article. A new concept of fractional-order passivity (FOP) is defined, which also contains the integer-order passivity. In the literature of multiweighted networks, many papers usually study its passivity only from the viewpoint of outer coupling matrices (OMs), which are also assumed to be connected and undirected. In this article, we add the viewpoint of inner coupling matrices (IMs), and the OMs can be directed and not connected, which can greatly improve the existing results. By means of decomposing IMs into their main diagonal matrices and residual matrices, we obtain that if the weighted combination of multiple OMs for each dimension is strongly connected, then FOP can be realized. Of course, the above results also hold for diagonal IMs, which is commonly addressed in previous works. Moreover, synchronization, adaptive coupling strengths and pinning control are also discussed. Besides, FOP and control rules for multiweighted and directed fractional-order reaction-diffusion network systems (MDFORDNSs) are derived by applying this strategy. Numerical examples are ultimately employed to examine the effectiveness of these gained results.