Control law synthesis for distributed multi-agent systems: Application to active clock distribution networks

In this paper, the problem of active clock distribution network synchronization is considered. The network is made of identical oscillators interconnected through a distributed array of phase-locked-loops (PLLs). The problem of the PLL network design is reformulated, from a control theory point of view, as a control law design for a distributed multi-agent system. Inspired by the decentralized control law design methodology using the dissipativity input-output approach, the particular topology of interconnected subsystems is exploited to solve the problem by applying a convex optimization approach involving simple Linear Matrix Inequality (LMI) constraints. After choosing the dissipativity properties which is satisfied by the interconnection matrix, the constraints are transformed into an H_∞ norm constraint on a particular transfer function that must be fulfilled for global stability. Additional constraints on inputs and outputs are introduced in order to ensure the desired performance specifications during the H_∞ control design procedure.