Robust and nonfragile consensus of positive multiagent systems via observer-based output-feedback protocols

This article investigates the consensus problem for positive multiagent systems via an observer-based dynamic output-feedback protocol. The dynamics of the agents are modeled by linear positive systems and the communication topology of the agents is expressed by an undirected connected graph. For the consensus problem, the nominal case is studied under the semidefinite programming framework while the robust and nonfragile cases are investigated under the linear programming framework. It is required that the distributed state-feedback controller and observer gains should be structured to preserve the positivity of multiagent systems. Necessary and/or sufficient conditions for the analysis of consensus are obtained by using positive systems theory and graph theory. For the nominal case, necessary and sufficient conditions for the codesign of state-feedback controller and observer of consensus are derived in terms of matrix inequalities. Sufficient conditions for the robust and nonfragile consensus designs are derived and the codesign of state-feedback controller and observer can be obtained in terms of solving a set of linear programs. Numerical simulations are provided to show the effectiveness and applicability of the theoretical results and algorithms.