This study addresses a challenging problem on the consensus of multi-agent systems, that is, simultaneously deals with the high-order linear multi-agent systems (including single and double integrators, and harmonic oscillators) and time-varying interaction topology. The interaction topology is assumed to switch among a finite number of connected undirected graphs having a non-vanishing dwell time. It is also constrained that each agent can use only the system outputs of its neighbouring agents for the purpose of feedback. Under these conditions, the authors propose two high-gain dynamic consensus protocols, one with multiple time-scale based and the other single time-scale, for the uniform rank systems without finite zeros. An example is provided to validate the proposed protocols.

Control of tasks by Flexible Joint Robots (FJR) is highly susceptible to disturbances, coupling, and vibrations that result from joint elasticity. A possible solution to this problem is a Disturbance Observer (DOB), which can address these issues in the joint space. However, this approach has limitations for workspace motion control, as the effect of nonlinear link dynamics and workspace coupling force is not considered. For these reasons, a novel DOB design for FJR in the workspace is deemed necessary, yet most research has focused on the joint DOB design. In this letter, a novel approach to modeling and control of the FJR in the workspace is proposed. A robust workspace nonlinear DOB for FJR is developed, taking into consideration the coupled dynamics of FJR as well as various disturbances that deteriorate the workspace position control, such as motor/link side disturbance, inertia variation, and workspace coupling force. In addition, the singularity problem that arises from modeling FJR for workspace DOB is accounted for by the proposed method. The effectiveness of the proposed method is demonstrated through simulations and experiments, and its stability is also verified.