Invariants for LTI systems with uncertain input

  • Authors:

  • Paul Hänsch;Stefan Kowalewski

  • Affiliations:

  • Embedded Software Laboratory, RWTH Aachen University, Germany;Embedded Software Laboratory, RWTH Aachen University, Germany

  • Venue:
  • RP'12 Proceedings of the 6th international conference on Reachability Problems
  • Year:
  • 2012

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Abstract

We propose a new method to derive invariants for LTI systems with uncertain inputs, i.e. systems of the form $\dot x(t) = Ax(t) + Bu(t)$ with state vector x(t)∈ℝn and uncertain input u(t)∈ℝm bounded by u(t)∈U⊆ℝm for all t≥0. Our approach is based on the real canonical form and the resulting invariants are conjunctions of bounds on linear and quadratic forms in the state variables x(t).