Feedback control problems for linear periodic systems (LPSs) with intervaltype parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality (LMI) for the asymptotical stability and state feedback stabilization, respectively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and suffcient.
This paper studies the consensus problems for a group of agents with switching topology and time-varying communication delays,where the dynamics of agents is modeled as a high-order integrator.A linear distributed consensus protocol is proposed,which only depends on the agent's own information and its neighbors'partial information.By introducing a decomposition of the state vector and performing a state space transformation,the closed-loop dynamics of the multi-agent system is converted into two decoupled subsystems.Based on the decoupled subsystems,some sufficient conditions for the convergence to consensus are established,which provide the upper bounds on the admissible communication delays.Also,the explicit expression of the consensus state is derived.Moreover,the results on the consensus seeking of the group of high-order agents have been extended to a network of agents with dynamics modeled as a completely controllable linear time-invariant system.It is proved that the convergence to consensus of this network is equivalent to that of the group of high-order agents.Finally,some numerical examples are given to demonstrate the effectiveness of the main results.
Fangcui JIANG,Long WANG,Guangming XIE(Institute of Intelligent Engineering,Center for Systems and Control,College of Engineering,and Key Laboratory of Machine Perception(Ministry of Education),Peking University,Beijing 100871,China)
This paper investigates the controllability of multi-agent systems based on agreement protocols. First, for a group of single-integrator agents, the controllability is studied in a unified framework for both networks with leader-following structure and networks with undirected graph. Some new necessary/sufficient conditions for the controllability of networks of single-integrator agents are established. Second, we prove that, under the same topology and same prescribed leaders, a network of high-order dynamic agents is completely controllable if and only if so is a network of single-integrator agents. Third, how the selection of leaders and the coupling weights of graphs affect the controllability is analyzed. Finally, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.
In this paper, using game theoretic ideas, we propose a modified snowdrift game to study the emergence and evo...
Chen Wang 1,2 , Bin Wu 2 , Ming Cao 1 , Guangming Xie 2 1. Faculty of Mathematics and Natural Sciences, ITM, University of Groningen, the Netherlands 2. Intelligent Control Laboratory, College of Engineering, Peking University, Beijing, China
