Abstract
A formation control problem for second-order multiagent systems with time-varying delays is considered. First, a leader-following consensus protocol is proposed for theoretical preparation. With the help of Lyapunov-Krasovskii functional, a sufficient condition under this protocol is derived for stability of the multiagent systems. Then, the protocol is extended to the formation control based on a multiple leaders’ architecture. It is shown that the agents will attain the expected formation. Finally, some simulations are provided to demonstrate the effectiveness of our theoretical results.
Highlights
Recent years have witnessed a rapidly growing interest in coordinated control of multiagent systems due to its broad applications in various disciplines [1,2,3,4,5,6,7,8,9,10,11,12]
For formation control with time delays, Luo et al [19] gave a sufficient condition of formation control of multiagent systems by using Lyapunov stability theory
With time-varying delays existing in the transmission of both velocity and position, we provide the following consensus protocol: ui (t)
Summary
Recent years have witnessed a rapidly growing interest in coordinated control of multiagent systems due to its broad applications in various disciplines [1,2,3,4,5,6,7,8,9,10,11,12]. The authors in [18] investigated the leader-following formation control problems for nonlinear systems under fixed and switching topologies. For formation control with time delays, Luo et al [19] gave a sufficient condition of formation control of multiagent systems by using Lyapunov stability theory. Lu et al [21] studied the formation control of second-order multiagent systems with time-varying delays, where the time delays existed only in the transmission of position information between neighbors. Motivated by the above analysis, we consider a leaderfollowing formation control problem for second-order multiagent systems, with time-varying delays existing in the transmission of both velocity and position. The superscripts “T” and “−1” stand for its transposition and inverse, respectively; Λ(⋅) and ‖ ⋅ ‖ denote the set of all eigenvalues and the spectral norm of the matrix, respectively. For a complex number μ ∈ C, Re(μ), Im(μ), and |μ| are its real part, imaginary part, and modulus, respectively. ⊗ denotes the Kronecker product
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