Admissible consensus for descriptor multi-agent systems via distributed observer-based protocols

In this paper, the admissible consensus problem of descriptor multi-agent systems via distributed observer-based protocols is considered. The dynamics of agents is modeled by the general form of continuous-time linear descriptor systems, and the interaction topology among the agents is modeled by a directed graph. It is assumed that the output information but not the state information of the agents is available. To achieve control objective, two types of state observers are adopted for the agents to estimate its states and the related state disagreements respectively, by which two different architectures of connecting observers and controllers are proposed. Based on the generalized Riccati equation and Lyapunov admissible theory, a sufficient admissible consensus condition is established for the descriptor multi-agent systems. The full-order and reduced-order observer-based consensus protocols can be unified in our proposed framework. Based on the special solutions of the established condition, some full-order and reduced-order observer-based consensus protocols can be obtained. Finally, a simple simulation example is provided to illustrate our established result.