A new approach for the model updating of $(\star ,\epsilon )$-palindromic systems with no spill-over

Abstract

In this paper, model updating problem of the $(\star ,\epsilon )$-palindromic system with no spill-over (PMUP) is considered. First, we drive the spectral decomposition of $(\star ,\epsilon )$-palindromic quadratic matrix polynomial $P(\lambda )$ by a standard pair $(X,J)$ and a parameter matrix $\Gamma$. And the structures of $\Gamma$ are provided when $J$ is assumed to be a block diagonal matrix. Using the spectral decomposition of $P(\lambda )$, a new sufficient solvable condition of the PMUP is provided and a set of analytical solutions is characterized. Finally, two algorithms are developed to address the cases of both simple and multiple eigenvalues. and the performance of our proposed method is illustrated by several numerical examples.