Fastest containment control of discrete-time multi-agent systems using static linear feedback protocol

This paper focuses on the fastest containment control of discrete-time single-input linear multi-agent systems (MASs) over directed graphs. By proving that the largest convergence region for containment control is identical to the largest gain margin of the discrete-time linear quadratic regulator (LQR) in the sense of a radial projection, the necessary and sufficient condition on the containment control problem is derived using a standard Riccati design method. Inspired by this, we introduce a speed factor to characterize the worst-case convergence speed of the containment control and show that the convergence speed becomes faster as the speed factor decreases. The analytical solutions of the fastest convergence speed are obtained, and static linear distributed protocols are designed using the standard algebra Riccati equation to achieve the fastest convergence speed of the containment control. Finally, a numerical example is given to verify the validity of the developed theoretical results.