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 suf-ficient 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 conver-gence speed are obtained, and static linear distributed protocols are designed using the standard algebra Riccati equation to achieve the fastest convergence speed of the contain-ment control. Finally, a numerical example is given to verify the validity of the developed theoretical results.(c) 2022 Elsevier Inc. All rights reserved.