Constrained H∞ Consensus of Second-Order Discrete-Time Multi-Agent Networks With Nonconvex Velocity Constraints

Abstract

This paper addresses the constrained H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus of second-order discrete-time multi-agent systems with nonconvex velocity constraints and external disturbances over a directed network. A novel nonlinear distributed control law is proposed to enable all agents converge to an agreement cooperatively while their velocities remain in different nonconvex constraint sets. To measure the effect of external disturbances on consensus, a nonlinear H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> output function is introduced via maximum and minimum functions. By a model transformation, the original closed-loop system is changed into an equivalent one. And then, the convergence analysis and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance analysis are completed by utilizing Lyapunov stability theory and robust control theory. In addition, the sufficient constrained H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus conditions are deduced in the form of matrix inequalities under the assumption of strong connectivity of directed network. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.