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.
%0 Thesis
%1 holicki2022complete
%A Holicki, T.
%D 2022
%K from:tobiasholicki pn4 imng exc2075
%R 10.18419/opus-12158
%T A Complete Analysis and Design Framework for Linear Impulsive and Related Hybrid Systems
%X 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.
@phdthesis{holicki2022complete,
abstract = {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.},
added-at = {2023-02-06T14:22:01.000+0100},
author = {Holicki, T.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2bb0bda50d7935d6609a447a74ccd1282/mathematik},
doi = {10.18419/opus-12158},
interhash = {3733059842f478e9cf76bc6b11fde90f},
intrahash = {bb0bda50d7935d6609a447a74ccd1282},
keywords = {from:tobiasholicki pn4 imng exc2075},
school = {University of Stuttgart},
timestamp = {2023-10-31T15:11:20.000+0100},
title = {A Complete Analysis and Design Framework for Linear Impulsive and Related Hybrid Systems},
year = 2022
}
