Modulated sampled-data consensus for networked Euler-Lagrange systems with differentiable pulse function

This paper is concerned with the sampled-data consensus of networked Euler-Lagrange systems. The Euler-Lagrange system has enormous advantages in analyzing and designing dynamical systems. Yet, some problems arise in the Euler-Lagrange equation-based control laws when they contain sampled-data feedbacks. The control law differentiates the discontinuous sampled-data signals to generate its control input. In this process, infinities in the control inputs are generated inevitably. The main goal of this work is to eliminate these infinities and make the control inputs applicable. To reach this goal, a class of differentiable pulse functions is designed for the controllers. The pulse functions work as multipliers on the sampled-data signals to make them differentiable, hence avoid the infinities. A new consensus condition compatible with the pulse function is also obtained through rigorous consensus analysis. The condition is proved to be less conservative compared with that of the existing method. Finally, numerical examples are given to illustrate the findings and theoretical results.