Robust output consensus of discrete‐time networked negative imaginary systems
Qian Zhang, Liu Liu, Yufeng Lu · Asian Journal of Control · 2021
Abstract This paper considers robust output consensus of discrete‐time networked homogeneous negative imaginary (NI) systems under ℓ2 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.