Path-complete positivity of switching systems

Forni, F.;Jungers, Raphaël;Sepulchre, R.
(2017) IFAC-PapersOnLine — Vol. 50, p. 4558-4563 (2017)

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Authors
  • Forni, F.University of Cambridge, United Kingdom
    Author
  • Jungers, RaphaëlUCLouvain
    Author
  • Sepulchre, R.University of Cambridge, United Kingdom
    Author
Abstract
The notion of path-complete positivity is introduced as a way to generalize the property of positivity from one LTI system to a family of switched LTI systems whose switching rule is constrained by a finite automaton. The generalization builds upon the analogy between stability and positivity, the former referring to the contraction of a norm, the latter referring to the contraction of a cone (or, equivalently, a projective norm). We motivate and investigate the potential of path-complete positivity and we propose an algorithm for the automatic verification of positivity.
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Forni, F., Jungers, R., & Sepulchre, R. (2017). Path-complete positivity of switching systems. IFAC-PapersOnLine, 50, 4558-4563. https://doi.org/10.1016/j.ifacol.2017.08.731 (Original work published 2017)