Simultaneous stabilization and synchronization for multi-agent systems via a low gain method

We study a simultaneous stabilization and synchronization (SSS) problem for one class of linear multi-agent systems with non-identical agents and a directed connection graph. The agent dynamics can be different and the orders of agents are not necessarily equal. We show that a single control loop can be designed for each agent to enable some agent states, named as internal states, to be stabilized while some other states, named as external states, to be synchronized. We design a distributed control law based on local measurements and partial information (external states only) exchanged from neighboring agents to enable SSS. To avoid internal state coupling in the SSS control law, a low gain approach is proposed for control law synthesis. Perturbation analysis, decoupling coordinate transformation, and weighted Laplacian are exploited for convergence and stability analysis. The sufficient conditions to achieve SSS are obtained, followed by specific approaches of designing the control gain matrices.