Browsing by Author "Holicki, Tobias"

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Open Access
A complete analysis and design framework for linear impulsive and related hybrid systems
(2022) Holicki, Tobias; Scherer, Carsten W. (Prof. Dr.)
We establish a framework for systematically analyzing and designing output-feedback controllers for linear impulsive and related hybrid systems that might even be affected by various types of uncertainties. In particular, the framework encompasses uncertain switched and sampled-data systems as well as networked systems with switching communication topologies. The framework is based on recently developed convex criteria involving a so-called clock for analyzing impulsive systems under dwell-time constraints. We elaborate on the extension of those criteria for dynamic output-feedback controller synthesis by means of convex optimization and generalize the so-called dual iteration to impulsive systems. The latter originally and still constitutes a promising heuristic procedure for the challenging and non-convex design of static output-feedback controllers for standard linear time-invariant systems. Moreover, for uncertain impulsive systems as modeled in terms of linear fractional representations, we generalize the nominal analysis criteria by providing novel robust analysis conditions based on a novel time-domain and clock-dependent formulation of integral quadratic constraints. Finally, by combining the insights on nominal synthesis and robust analysis, we are able to tackle challenging output-feedback designs of practical relevance, such as the design of gain-scheduled, robust or robust gain-scheduled controllers for impulsive systems. Most of the obtained analysis and synthesis conditions involve infinite-dimensional (differential) linear matrix inequalities which can be numerically solved by using relaxation methods based on, e.g., linear splines, B-splines or matrix sum-of-squares that we discuss as well.
Open Access
Revisiting and generalizing the dual iteration for static and robust output‐feedback synthesis
(2021) Holicki, Tobias; Scherer, Carsten W.
The dual iteration was introduced in a conference paper in 1997 by Iwasaki as an iterative and heuristic procedure for the challenging and non‐convex design of static output‐feedback controllers. We recall in detail its essential ingredients and go beyond the work of Iwasaki by demonstrating that the framework of linear fractional representations allows for a seamless extension of the dual iteration to output‐feedback designs of practical relevance, such as the design of robust or robust gain‐scheduled controllers. In the paper of Iwasaki, the dual iteration is solely based on, and motivated by algebraic manipulations resulting from the elimination lemma. We provide a novel control theoretic interpretation of the individual steps, which paves the way for further generalizations of the powerful scheme to situations where the elimination lemma is not applicable. As an illustration, we extend the dual iteration to a design of static output‐feedback controllers with multiple objectives. We demonstrate the approach with numerous numerical examples inspired from the literature.