https://ensta-bretagne.hal.science/hal-03164789Rauh, AndreasAndreasRauhLab-STICC_ROBEX - Equipe ROBotics for EXploration - Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance - ENIB - École Nationale d'Ingénieurs de Brest - UBS - Université de Bretagne Sud - UBO - Université de Brest - ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique - UBL - Université Bretagne Loire - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris]ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées BretagneKersten, JuliaJuliaKerstenUniversität RostockTransformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded ParametersHAL CCSD2021interval analysiscooperative system modelsreachability analysiswrapping effect[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Rauh, Andreas2021-03-10 10:54:532023-03-24 14:53:212021-03-10 11:11:21enJournal articleshttps://ensta-bretagne.hal.science/hal-03164789/document10.3390/a14030085application/pdf1Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.