Control of uncertain sampled-data systems
This research monograph provides a detailed treatment of uncertainty analysis for sampled-data systems in the context of systems control theory. Sampled-data systems refers to the hybrid system formed when continuous time and discrete time systems are interconnected. By uncertainty analysis the author means achievable performance in the presence of worst-case uncertainty and disturbances. The monograph evolved from the author's Ph.D. dissertation at Cambridge University. The theory is developed primarily in an operator-theoretic framework; the signal space of interest is \(L_2\). A significant portion of the monograph is devoted to analyzing robust stabilization with linear time-invariant (LTI) perturbations. The author develops a condition that characterizes robust stability to structured, and thus also unstructured, LTI perturbation. This robustness test is in terms of the structured singular values of an infinite-dimensional compact operator. The author also considers robust performance of sampled-data systems to structured perturbations. Solutions to these robust performance problems are pursued using the same operator-theoretic framework and machinery that is developed for the LTI robustness analysis. The main feature of each of these conditions is that they are finite-dimensional. The robust performance problem is also investigated with respect to three uncertainty classes: periodic, quasi-periodic, and arbitrary time-varying uncertainties.
scientific article; zbMATH DE number 833373