Necessary and Sufficient Conditions of Formation-Containment Control of High-Order Multiagent Systems With Observer-Type Protocols.
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The analysis and design problems of formation-containment control for high-order linear time-invariant (LTI) multiagent systems (MASs) on directed graphs with observer-based output-feedback protocols are given in this work. To expand the feasibility of state formation configuration, two well-structured compensation signals are introduced for the leaders and followers in the protocols, respectively. Benefitting from the compensation signal of followers, the decoupling between formation control of leaders and containment control of followers is achieved. Thus, a necessary and sufficient condition is first established such that the formation-containment control for high-order LTI MASs can be achieved. Moreover, a heuristic iterative algorithm is developed to compute the controller gains, observer gains, as well as the compensation signals. Finally, two numerical examples are implemented to illustrate the time-varying formation-containment control of high-order MASs, which shows the validity and practicability of the theoretical results and algorithm.