Positive Consensus of Directed Multiagent Systems

Positive Consensus for Heterogeneous Multi-agent Systems

“…Since we have to ensure a positive state constraint simultaneously, the problem is inherently nonlinear. In fact, only a few important attempts have been made in literature for a special case when A 0 = 0 (i.e., the consensus pattern is a constant point) and the agents are with identical dynamics under the name of positive consensus [19][20][21][22][23]26]. Compared with these results, this formulation takes positive state constraints, general consensus pattern, and heterogeneous agent dynamics together, which will make the problem much more challenging.…”

“…Remark 2 Compared with existing positive consensus results derived for homogeneous multi-agent systems in [19][20][21][22][23][24][25][26], we have removed such limitations and present a two-step design for this problem. This enables us to handle heterogeneous multi-agent systems whose dynamics can be different from each other in both system matrices and orders over switching communication topologies.…”

“…Note that the positive consensus problem was done in this work via solving a positive static output feedback stabilization problem for the whole multi-agent system. Further efforts along this technical line have been made in [20][21][22][23] using state feedback. Moreover, some authors considered dynamic rules to relax the conditions to ensure a positive consensus, e.g., [24][25][26].…”

Proportional‐derivative controller design of continuous‐time positive linear systems

“…Current research on positive systems, especially positive linear systems, could be roughly divided into three types, that is, positive controllability and controller design, 8,9 positive observability and observer design, 10 and positive realization. 11 In recent years, positive systems theory has also been combined with other branches of control theory, such as cooperative control 12,13 and time-delay systems. 14 More recently, the research interest of positive systems has focused on fairly different control issues, in particular, robust positive stabilization and system performance 15,16 , the bounded real lemma 17 and the Kalman-Yakubovic-Popov lemma 18 for positive systems, decentralized and distributed control.…”

“…Current research on positive systems, especially positive linear systems, could be roughly divided into three types, that is, positive controllability and controller design, 8,9 positive observability and observer design, 10 and positive realization 11 . In recent years, positive systems theory has also been combined with other branches of control theory, such as cooperative control 12,13 and time‐delay systems 14 …”