The Smallest Eigenvalue of the Generalized Laplacian Matrix, with Application to Network-Decentralized Estimation for Homogeneous Systems

H ∞-Control of Grid-Connected Converters: Design, Objectives and Decentralized Stability Certificates

“…On the one hand, the transfer function matrix F −1 (s)Y i (s) in (23) is solely related to the local frequency-domain dynamics of the ith device, as Y i (s) is the device's admittance matrix and F (s) is a fixed transfer function matrix determined by the line R/L ratio. On the other hand, λ 1 is determined by the network structure, which in fact, can be seen as the connectivity strength of the network because λ 1 can only increase when the network becomes denser [25]. With Proposition IV.1, there are two ways to ensure the stability of the multi-device system.…”

“…Given the weighting functions in Subsection III and the system parameters in Table I, we use the hinfstruct routine in MATLAB to solve the H ∞ -optimal control problem in (25), and the static parameter matrix K is obtained as…”

“…and W 53 (s) with different bandwidths (the blue ones have the lowest bandwidths and the yellow ones have the highest bandwidths). By solving the H ∞ -optimal control problem in (25) one obtains different H ∞ -optimal controller K. Fig.7 shows the time-domain responses of the active power when the different weighting functions are adopted, and it can be seen that all the responses have anticipated performance (no overshot). Moreover, increasing the bandwidths of W 83 (s) and W 53 (s) leads to faster response of the active power, that is, the H ∞ design provides a convenient and systematic way to achieve expected system dynamics.…”

A Bounded Complementary Sensitivity Function Ensures Topology-Independent Stability of Homogeneous Dynamical Networks

“…To prove the thesis, resort is made to the zero-exclusion theorem. Since the nominal system is stable because condition (14) implies (7), the stability of the uncertain system is ensured if the previous determinant is nonzero at s = ω for all admissible ∆ F and ∆ G . Now, dividing by F (ω)G(ω), this condition can be expressed as are diagonal matrices whose entries are bounded according to (11).…”

“…Many complex technological and natural systems can be effectively modelled as a large-scale network of dynamic subsystems that interact with one another either statically or dynamically. Distributed problems in several contexts can be formulated in this dynamical-network framework [11], spanning from the analysis of biological and chemical systems [29], [10], [2], [19], [12] to IT systems [28], including consensus [23], [26], synchronisation [9], coordination [15], [8], estimation [27], [7] and control [14], [4], [5], [6], [21] of multi-agent systems.…”