The paper is the first part of a series of papers which deal with realization theory for linear hybrid systems. Linear hybrid systems are hybrid systems in continuous-time without guards whose continuous dynamics is determined by linear control systems and whose the discrete dynamics is determined by a finite state automaton. In Part I of the current series of papers we will formulate necessary and sufficient conditions for the existence of a linear hybrid system realizing a specified set of input-output maps. We will also sketch a realization algorithm for computing a linear hybrid system from the input-output data. In Part II we will present conditions for observability and span-reachability of linear hybrid systems and we will show that minimality is equivalent to observability and span-reachability; we will also discuss algorithms for checking observability and span-reachability and for transforming a linear hybrid system to a minimal one.
Additional Metadata
Keywords hybrid systems, realization theory, Hankel-matrix, formal power series, automata
MSC Realizations from input-output data (msc 93B15), Minimal systems representations (msc 93B20), Algebraic methods (msc 93B25), Control systems (msc 93Cxx)
THEME Life Sciences (theme 5), Energy (theme 4)
Publisher CWI
Series Modelling, Analysis and Simulation [MAS]
Citation
Petreczky, M, & van Schuppen, J.H. (2008). Realization theory for linear hybrid systems, part I: Existence of realization. Modelling, Analysis and Simulation [MAS]. CWI.