Title: Input-dependent externally positive systems and their application to undershoot and overshoot analysis
Abstract: A linear time-invariant system is said to be externally positive if it maps non-negative inputs to non-negative outputs, for zero initial conditions. Although this property has proven useful in many applications, in certain cases we may be interested only in specific classes of inputs. For instance, preventing overshoot for all possible non-negative input signals is often unnecessary. Instead, we may want to restrict our attention to, e.g., step inputs. Motivated by this, we generalize the notion of externally positive systems by introducing input-dependent externally positive systems, i.e., systems that map specific inputs, to non-negative outputs. We show how this class of systems is a natural generalization of externally positive systems, by extending well-known necessary and sufficient conditions to the input-specific case. Finally, we leverage this new class of systems to derive necessary and sufficient conditions to determine the presence of overshoot and undershoot in linear time-invariant feedback control systems.
Bio: Sebastiaan van den Eijnden received the Ph.D. degree from the Eindhoven University of Technology (TU/e) in 2022. From 2021–2023, he has been working as a mechatronics and control engineer at ASML, the Netherlands. Currently, Sebastiaan is an Assistant Professor at the department of Mechanical Engineering, TU/e. His research interests include nonlinear and hybrid systems, input-output stability theory, robust control, graphical methods for nonlinear control system analysis and design, as well as data-based and learning control for mechatronic systems.
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