Model reduction of linear multi-agent systems by clustering with $$\varvec{\mathcal {H}_2}$$ H 2 and $$\varvec{\mathcal {H}_\infty }$$ H ∞ error bounds

Abstract

Firstly, we will establish an a priori upper bound for the H 2 model reduction error in case that the agent dynamics is an arbitrary multivariable input-state-output system. Secondly, for the single integrator case, we will derive an explicit formula for the H ∞ model reduction error. Thirdly, we will prove an a priori upper bound for the H ∞ model reduction error in case that the agent dynamics is a symmetric multivariable input-state-output system. Finally, we will consider the problem of obtaining a priori upper bounds if we cluster using arbitrary, possibly non almost equitable, partitions.