Robust output consensus of networked negative imaginary systems via an integral quadratic constraint approach

Abstract

This paper deals with the robust output consensus problem of networked homogeneous and heterogeneous negative imaginary (NI) systems under external disturbances via the integral quadratic constraint (IQC) approach. Applying the IQC-based NI stability result and properties of the network graph, a necessary and sufficient IQC-based condition is given for robust output consensus of networked homogeneous NI systems without poles at the origin. This condition depends on the corresponding complementary IQCs at zero and infinite frequencies as well as all eigenvalues of the Laplacian matrix associated with the network graph, and it covers the dc loop gain condition in the earlier literature by constructing appropriate IQC multipliers. Moreover, the robust output consensus can be preserved along a path by IQC-based conditions. Subsequently, the robust output consensus problem is also considered for homogeneous NI systems having poles at the origin by adding an assumption related to the largest eigenvalue of the Laplacian matrix. Besides, sufficient IQC-based conditions for the heterogeneous case are described by different IQC multipliers. Finally, some examples are shown to illustrate the main results.