Stability radii of delay difference systems under affine parameter perturbations in infinite dimensional spaces
The authors investigate the stability radii for delay difference systems in infinite-dimensional spaces described by a linear difference equation of the form: \[ x(t+ K+ 1)= A_0 x(t+ K)+ A_1 x(t+ K-1) +\cdots+ A_k x(t),\quad t,K\in\mathbb{N}, \] where \(A_i\in{\mathcal L}(X)\), \(i\in \overline K= \{0,1,\dots, K\}\) under arbitrary parameters of the form \[ A_i\mapsto A_i+ \sum^N_{j=1} D_{ij}\Delta_{ij} E_{ij},\quad i\in\overline K \] and \[ A_i\mapsto A_i+ \sum^N_{j=1} \delta_{ij} A_{ij},\quad i\in\overline K, \] where \(D_{ij}\in{\mathcal L}(U_{ij}, X)\), \(E_{ij}\in{\mathcal L}(X, Y_{ij})\) and \(A_{ij}\in{\mathcal L}(X)\), \(i\in\overline K\), \(j\in\overline N= \{1,2,\dots, N\}\) are given operators defining the scaling and structure of the parameter uncertainties, and \(A_{ij}\in{\mathcal L}(Y_{ij}, U_{ij})\) and \(\delta_{ij}\) are, respectively, unknown operators and scalar representing parameter uncertainties.
scientific article; zbMATH DE number 5321647