Synchronization of a network of oscillators with delays in the case of 1-D smart antennas array: a passivity analysis approach

In this paper, networks of oscillators are studied in the case of 1D antennas array. Each oscillator of the network is associated to an antenna. In this case, time delays are introduced between oscillator outputs in order to modify the spatial gain of the antenna array. The unidirectionally coupled network has not be investigated in smart antenna array. Firstly, the structure is proposed with hyper-frequency elements and secondly, a new analysis tool is presented to study the stability. The delay effects on the network synchronization are tackled and it is assumed that the parameters of the oscillators are in a polytope. Using Lyapunov methods and LMI (linear matrix inequality) framework and the dissipativity theory, a new condition is given to ensure global exponential synchronization. A validation is made in simulation with Matlab.