TY - GEN
T1 - Exact Stability Analysis of the Second-Order Affine Formation Maneuver System with Three Independent Time Delays
AU - Zhang, Xujie
AU - Gao, Qingbin
AU - Cai, Jiazhi
N1 - Publisher Copyright:
© 2023 Technical Committee on Control Theory, Chinese Association of Automation.
PY - 2023
Y1 - 2023
N2 - We investigate the asymptotic stability of a leader-follower type second-order affine formation maneuver system with three independent time delays. These three delays stem from the communication channels of position, velocity, and acceleration. The central idea is to exactly determine the potential stability switching loci in the domain of delays, namely the kernel and offspring hypersurfaces (KOH). For this, we first decompose the system's characteristic equation into a sequence of factors through a factorization procedure. We then adopt the Dixon resultant theory combining the frequency sweeping technique to ascertain KOH of each subsystem exhaustively. Finally, we superpose all KOH and resort to the Cluster Treatment of Characteristic Roots (CTCR) paradigm to create the complete stability map of the whole system. Finally, we provide a case study to demonstrate the effectiveness of these methodologies and point out the positive and negative effects of the delays on the affine formation system.
AB - We investigate the asymptotic stability of a leader-follower type second-order affine formation maneuver system with three independent time delays. These three delays stem from the communication channels of position, velocity, and acceleration. The central idea is to exactly determine the potential stability switching loci in the domain of delays, namely the kernel and offspring hypersurfaces (KOH). For this, we first decompose the system's characteristic equation into a sequence of factors through a factorization procedure. We then adopt the Dixon resultant theory combining the frequency sweeping technique to ascertain KOH of each subsystem exhaustively. Finally, we superpose all KOH and resort to the Cluster Treatment of Characteristic Roots (CTCR) paradigm to create the complete stability map of the whole system. Finally, we provide a case study to demonstrate the effectiveness of these methodologies and point out the positive and negative effects of the delays on the affine formation system.
KW - Affine transformation
KW - Formation maneuver control
KW - Multiple delays
KW - Stability analysis
KW - Time-delay systems
UR - https://www.scopus.com/pages/publications/85175568745
U2 - 10.23919/CCC58697.2023.10239847
DO - 10.23919/CCC58697.2023.10239847
M3 - 会议稿件
AN - SCOPUS:85175568745
T3 - Chinese Control Conference, CCC
SP - 5529
EP - 5534
BT - 2023 42nd Chinese Control Conference, CCC 2023
PB - IEEE Computer Society
T2 - 42nd Chinese Control Conference, CCC 2023
Y2 - 24 July 2023 through 26 July 2023
ER -