The Lyapunov Theorem: Its extensions and applications

1990 ◽  
pp. 84-103 ◽  
Author(s):  
Czesraw Olech
Keyword(s):  
Lyapunov Theorem

scholarly journals Adaptive 3D Distance-Based Formation Control of Multiagent Systems with Unknown Leader Velocity and Coplanar Initial Positions

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Xuejing Lan ◽  
Wenbiao Xu ◽  
Yun-Shan Wei
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Relative Position ◽  
Formation Control ◽  
Control Law ◽  
Asymptotically Stable ◽  
Coordinate Systems ◽  
Lyapunov Theorem ◽  
Globally Asymptotically Stable ◽  
3 Dimensional

This paper considers the distributed 3-dimensional (3D) distance-based formation control of multiagent systems, where the agents are connected based on an acyclic minimally structural persistent (AMSP) graph. A parameter is designed according to the desired formation shape and is used to solve the problem that there are two formation shapes satisfying the same distance requirements. The unknown moving velocity of the leader agent is estimated adaptively by the followers requiring only the relative position measurements with respect to their local coordinate systems. In addition, the proposed formation controller provides a new way for the agent to leave the initial coplanar location. The 3D formation control law is globally asymptotically stable and has been demonstrated based on the Lyapunov theorem. Finally, two numerical simulations are presented to support the theoretical analysis.

803 Analysis of local stability for nolinear systems via a dual of Lyapunov Theorem

2006 ◽  
Vol 2006.44 (0) ◽  
pp. 303-304
Author(s):  
Yutaka dohi ◽  
Izumi Masubuchi ◽  
Masami Saeki
Keyword(s):  
Local Stability ◽  
Lyapunov Theorem
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