Robust output consensus of discrete-time networked negative imaginary systems

This paper considers robust output consensus of discrete-time networked homogeneous negative imaginary (NI) systems under l(2) external disturbances via integral quadratic constraints (IQCs). A necessary and sufficient condition for robust output consensus of discrete-time networked NI systems without poles at +/- 1 is obtained by the IQC-based discrete-time NI (D-NI) stability result. Moreover, the robust output consensus problem can be solved by designing an unstable controller whose poles are related to transmission zeros of D-NI systems. The case of discrete-time networked NI systems with poles at 1 is also studied. These main results are related to all eigenvalues of the Laplacian matrix of the network graph as well as the corresponding complementary IQCs at +/- 1 frequencies. Some corollaries are given by constructing appropriate IQC multipliers in order to simplify the main results. Finally, three examples are shown to explain the validity of the main results.