In this study the swarm stability problem of high-order linear time-invariant (LTI) swarm systems with directed graph topology is dealt with. Consensus can be regarded as a specific type of swarm stability problem. Necessary and sufficient conditions for both swarm stability and consensus are presented. These conditions depend on the graph topology, the dynamics of agents and the interactions among the neighbours. Simulation instances are shown to illustrate the theoretical results.

In this paper, novel adaptive sliding mode dynamic controller with integrator in the loop is proposed for nonholonomic wheeled mobile robot (WMR). The modified kinematics controller is used to generate kinematics velocities of WMR which are subsequently used as the input to adaptive dynamic controller. Actuator dynamics are also derived to generate actuator voltage of WMR through torque and velocity vectors. Stability of both kinematics and dynamic controller is presented using Lyapunov stability analysis. The proposed scheme is verified and validated using computer simulations for tracking the desired trajectory of WMR. The performance of proposed scheme is compared with standard backstepping kinematics controller and classical sliding mode control. In addition, the performance is further compared with standard backstepping kinematics controller with adaptive sliding mode controller without integrator. It is shown that the proposed scheme exhibits zero steady state error, fast error convergence and robustness in the presence of continuous disturbances and uncertainties.

The controllability problem of high-order linear time-invariant (LTI) continuous-time swarm systems is investigated. A necessary and sufficient condition for complete controllability of homogeneous swarm systems is given. The controllability of graph is important and is analysed in detail. The concept of formation controllability is proposed and the relationship between complete controllability and formation controllability is studied.

This paper presents a novel approach for clustering, which is based on quasi-consensus of dynamical linear high-order multiagent systems. The graph topology is associated with a selected multiagent system, with each agent corresponding to one vertex. In order to reveal the cluster structure, the agents belonging to a similar cluster are expected to aggregate together. To establish the theoretical foundation, a necessary and sufficient condition is given to check the achievement of group consensus. Two numerical instances are furnished to illustrate the results of our approach.