We deal with the state consensus problem of a general Linear Interconnected Multi-Agent System （LIMAS） under a time-invariant and directed communication topology. Firstly, we propose a linear consensus protocol in a general form, which consists of state feedback of the agent itself and feedback form of the relative states between the agent and its neighbors. Secondly, a state-linear-transformation is applied to equivalently transform the state consensus problem into a partial stability problem. Based on the partial stability theory, we derive a sufficient and necessary criterion of consensus convergence, which is expressed via the Hurwitz stability of a real matrix constructed from the parameters of the agent models and the protocols, and present an analytical formula of the consensus function. Lastly, we propose a design procedure of the gain matrices in the protocol by solving a bilinear matrix inequality.
A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.
Alexander ALEKSANDROVElena ALEKSANDRO VAAlexey ZHABKO陈阳舟
