Algebraic Necessary and Sufficient Conditions for the Controllability of Conewise Linear Systems

Camlibel, M. K., Heemels, W. P. M. H. M. & Schumacher, J. M. H., Apr-2008, In : IEEE Transactions on Automatic Control. 53, 3, p. 762-774 13 p.

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The problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e., systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered fromour main result. Our treatment employs tools both from geometric control theory and mathematical programming.
Original languageEnglish
Pages (from-to)762-774
Number of pages13
JournalIEEE Transactions on Automatic Control
Issue number3
Publication statusPublished - Apr-2008


  • conewise linear systems, controllability, hybrid systems, piecewise linear systems, push-pull systems, reachability, COMPLEMENTARITY SYSTEMS, HYBRID SYSTEMS, OBSERVABILITY, NETWORKS

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