Eur. Phys. J. Special Topics 223, 757-772 (2014)
https://doi.org/10.1140/epjst/e2014-02139-5

Regular Article

Robust output synchronization of second-order systems

¹ Center for Scientific Research and Higher Education at Ensenada, BC, Electronics Department, Mexico
² Autonomous University of Baja California, Engineering Faculty, Mexico

^a e-mail: jqalvar@cicese.mx
^b e-mail: jcuesta@cicese.mx
^c e-mail: drosas@uabc.edu.mx

Received: 3 March 2014
Revised: 18 March 2014
Published online: 28 April 2014

Abstract

A technique to synchronize a network of dynamical systems described by second-order ordinary differential equations is presented. Each system can be driven by a coupling control signal, which is synthesized such that, at steady-state, the outputs of two given systems, say y_i and y_j, i≠j, satisfy a specified ratio, that is, y_i/y_j = α_i/α_j, α_i≠0≠α_j. Among others, this includes the cases where the outputs are synchronized in-phase or anti-phase. The proposed synchronization technique is robust; this means that a small synchronization error is preserved at steady-state, even if the systems were perturbed by external disturbances. Some level of parameter uncertainty can also be tolerated. The coupling control signals are synthesized based on a classical controller and a robust observer that estimates the generalized velocities and provides an estimation of the perturbation terms. Some experimental results, showing the performance of the proposed synchronization technique, are included.