Undamped nonlinear consensus using integral Lyapunov functions

Abstract

Abstract-This paper analyzes a class of nonlinear consensus algorithms where the input of an agent can be decoupled into a product of a gain function of the agents own state, and a sum of interaction functions of the relative states of its neighbors. We prove the stability of the protocol for both single and double integrator dynamics using novel Lyapunov functions, and provide explicit formulas for the consensus points. The results are demonstrated through simulations of a realistic example within the framework of our proposed consensus algorithm.

On distributed finite-time observer design and finite-time coordinated tracking of multiple double integrator systems via local interactions

“…Following a similar analysis as in the proof of Theorem 1 of [36], we can show that, under the condition that Assumption 1 holds at each time t , S y1 S S y2 ¤ ; for the case of V 1 .y.t // > 0 at each time t . We next consider three different cases to analyze the time derivative of V 1 .…”

“…Under the condition that Assumption holds at each time t , it is trivial to show that and V 1 ( y ) = 0 if and only if y 1 = y 2 = ⋯ = y n = 0 from the facts that and min i = 0,1, ⋯ , n { y i } ⩽ 0. Motivated by , we construct the following sets , . Following a similar analysis as in the proof of Theorem of , we can show that, under the condition that Assumption holds at each time t , …”

“…Under the condition that Assumption 1 holds at each time t , it is trivial to show that V 1 .y/ > 0 and V 1 .y/ D 0 if and only if y 1 D y 2 D D y n D 0 from the facts that max i D0,1, ,n ¹y i º > 0 and min i D0,1, ,n ¹y i º 6 0. Motivated by [36], we construct the following sets…”

Distributed finite‐time formation control for multiple quadrotors via local communications

“…Following a similar analysis as in the proof of theorem 1 of Andreasson et al, 37 it is trivial to show that, under the condition that Assumption 2 holds, S 1 ∪ S 2 ≠ ∅ for the case of W 1 ( hu ) > 0. S 1 ∪ S 2 ≠ ∅ can be divided into three different cases: S 1 ≠ ∅, S 2 = ∅ and S 1 = ∅, S 2 ≠ ∅ and S 1 ≠ ∅, S 2 ≠ ∅.…”

“…Motivated by Meng et al, we construct the following sets: , . Following a similar analysis as in the proof of theorem 1 of Andreasson et al, it is trivial to show that, under the condition that Assumption 2 holds, S 1 ∪ S 2 ≠∅ for the case of W 1 ( ε hu )>0. S 1 ∪ S 2 ≠∅ can be divided into three different cases: S 1 ≠∅, S 2 =∅ and S 1 =∅, S 2 ≠∅ and S 1 ≠∅, S 2 ≠∅.…”