TY - JOUR
T1 - Gain margin and Lyapunov analysis of discrete-time network synchronization via Riccati design
AU - Zhang, Liangyin
AU - Chen, Michael Z. Q.
AU - Zou, Yun
AU - Chen, Guanrong
PY - 2023/9/4
Y1 - 2023/9/4
N2 - This paper deals with solution analysis and gain margin analysis of a modified algebraic Riccati matrix equation, and the Lyapunov analysis for discrete-time network synchronization with directed graph topologies. First, the structure of the solution to the Riccati equation associated with a single-input controllable system is analyzed. The solution matrix entries are represented using unknown closed-loop pole variables that are solved via a system of scalar quadratic equations. Then, the gain margin is studied for the modified Riccati equation for both multi-input and single-input systems. A disc gain margin in the complex plane is obtained using the solution matrix. Finally, the feasibility of the Riccati design for the discrete-time network synchronization with general directed graphs is solved via the Lyapunov analysis approach and the gain margin approach, respectively. In the design, a network Lyapunov function is constructed using the Kronecker product of two positive definite matrices: one is the graph positive definite matrix solved from a graph Lyapunov matrix inequality involving the graph Laplacian matrix; the other is the dynamical positive definite matrix solved from the modified Riccati equation. The synchronizing conditions are obtained for the two Riccati design approaches, respectively. © 2023 John Wiley & Sons Ltd.
AB - This paper deals with solution analysis and gain margin analysis of a modified algebraic Riccati matrix equation, and the Lyapunov analysis for discrete-time network synchronization with directed graph topologies. First, the structure of the solution to the Riccati equation associated with a single-input controllable system is analyzed. The solution matrix entries are represented using unknown closed-loop pole variables that are solved via a system of scalar quadratic equations. Then, the gain margin is studied for the modified Riccati equation for both multi-input and single-input systems. A disc gain margin in the complex plane is obtained using the solution matrix. Finally, the feasibility of the Riccati design for the discrete-time network synchronization with general directed graphs is solved via the Lyapunov analysis approach and the gain margin approach, respectively. In the design, a network Lyapunov function is constructed using the Kronecker product of two positive definite matrices: one is the graph positive definite matrix solved from a graph Lyapunov matrix inequality involving the graph Laplacian matrix; the other is the dynamical positive definite matrix solved from the modified Riccati equation. The synchronizing conditions are obtained for the two Riccati design approaches, respectively. © 2023 John Wiley & Sons Ltd.
KW - directed graph
KW - gain margin
KW - Lyapunov function
KW - multi-agent network
KW - Riccati equation
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85169833375&origin=recordpage
U2 - 10.1002/rnc.6974
DO - 10.1002/rnc.6974
M3 - RGC 21 - Publication in refereed journal
JO - International Journal of Robust and Nonlinear Control
JF - International Journal of Robust and Nonlinear Control
SN - 1049-8923
ER -