Poset-causal systems form a class of decentralized systems introduced by Shah and Parrilo (47th IEEE conference on decision and control, IEEE, 2008) and studied mainly in the context of optimal decentralized control. In this paper, we develop part of the realization theory for poset-causal systems. More specifically, we investigate several notions of controllability and observability, and their relation under duality. These new notions extend concepts of controllability and observability in the context of coordinated linear systems (Kempker et al. in Linear Algebra Appl 437:121–167, 2012). While for coordinated linear systems there is a clear hierarchical structure with a single (main) coordinator, for poset-causal systems there need not be a single coordinator, and the communication structure between the decentralized systems allows for more intricate structures, governed by partial orders. On the other hand, we show that the class of poset-causal systems is closed under duality, which is not the case for coordinated linear systems, and that duality relations between the various notions of observability and controllability exist.

准集因果系统是Shah和Parrilo（第47届IEEE决策与控制会议，IEEE，2008年）引入的一类分散系统，主要在最佳分散控制的背景下进行研究。在本文中，我们开发了因果因果系统的部分实现理论。更具体地说，我们研究了可控性和可观察性的几种概念，以及它们在对偶关系下的关系。这些新概念扩展了协调线性系统中可控性和可观察性的概念（Kempker等人在Linear Algebra Appl 437：121–167，2012）。对于线性协调系统，有一个清晰的层次结构，其中只有一个（主）协调器，而对于因果关系系统，则不需要一个协调器，分散系统之间的通信结构允许由部分订单控制的更复杂的结构。另一方面，我们表明，姿势-因果系统的类别在对偶关系下是封闭的，而对于线性协调系统则不是这种情况，并且在可观察性和可控制性的各种概念之间存在对偶关系。