Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations
The authors consider the time delay control system with uncertainties \[ \dot{x}(t) = (A_0+\sum_{i=1}^mk_i(t)A_i+\widetilde{A}(t))x(t) + \sum_{\ell=1}^h\sum_{i=1}^m k_i(t)[A_{\ell i}x(t-\tau_\ell) +B_{\ell i}u(t-\tau_\ell)] + \] \[ + (B_0+\sum_{i=1}^mk_i(t)B_i+\widetilde{B}(t))u(t) \] \[ y = (C_0+\sum_{i=1}^mk_i(t)C_i+\widetilde{C}(t))x(t) \] with \(k_i(t)\) accounting for structured uncertainties and \(\widetilde{A}\), \(\widetilde{B}\), \(\widetilde{C}\) for bounded unstructured uncertainties. This system is subject to the static output controller \(u = Ky\). Some sufficient robust stability conditions are obtained using a standard quadratic Lyapunov functional of the form \[ V(\phi) = \phi^T(0)P\phi(0) + \sum_1^h\int_{-\tau_j}^0\phi^T(\theta)D_j\phi(\theta)d\theta. \] Some examples of academic type are discussed and a comparison to previous known results is given.
scientific article; zbMATH DE number 2136791