Upper solution bound of the CCARE and its application in multi-agent systems with time-delay in the state

Abstract

Stability is important for control systems. In this paper, using the transformation of the matrix equations and some significant properties of the matrix inequality, we derived new upper solution bounds of the continuous coupled algebraic Riccati equation (CCARE). The new bounds are more precise than those proposed in some existing works on this topic numerically. Next, a condition for the stability of multi-agent systems with time-delay in the state is presented according to the upper solution bound of the CCARE. Finally, corresponding numerical examples are provided to illustrate the superior and effectiveness of the derived results.

Keywords:

• Continuous coupled algebraic Riccati equation
• solution bounds
• multi-agent systems
• time-delay
• stability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported in part by National Natural Science Foundation for Youths of China [grant number 11801164], National Natural Science Foundation of China [grant numbers 11971413, 11571292], the Key Project of National Natural Science Foundation of China [grant number 91430213], the General Project of Hunan Provincial Natural Science Foundation of China [grant number 2015JJ2134], and the General Project of Hunan Provincial Education Department of China [grant number 15C1320].