Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states. Then by following a proper protocol, the state-dependent dynamic graph is driven to a pre-specified structure. The main results are derived via Lasalle's Invariant Principle and numerical examples that find very good agreements with the analytical results are also included.
In this paper, the static output feedback stabilization (SOFS) of deterministic finite automata (DFA) via the semi-tensor product (STP) of matrices is investigated. Firstly, the matrix expression of Moore-type automata is presented by using STP. Here the concept of the set of output feedback feasible events (OFFE) is introduced and expressed in the vector form, and the stabilization of DFA is defined in the sense of static output feedback (SOF) control. Secondly, SOFS problem of DFA is investigated within the framework of STP, including single-equilibrium-based SOFS, multi-equilibrium-based SOFS, and further limit cycle-based SOFS. Then the necessary and sufficient conditions for the existence of the three types SOFS are proposed respectively. Meanwhile the efficient and systematic procedures based on the matrix theory to seek the corresponding SOF controller are provided for the three types SOFS problem. Finally, two examples are presented to illustrate the effectiveness of the proposed approach.