Exponential stability of switched hyperbolic systems in a bounded domain
Saurabh Amin, Falk Hante, Alexandre Bayen

Citation
Saurabh Amin, Falk Hante, Alexandre Bayen. "Exponential stability of switched hyperbolic systems in a bounded domain". Technical report, UC Berkeley, 2008.

Abstract
We consider switching in time among a finite family of systems governed by linear hyperbolic partial differential equations on a bounded space interval. The switching system is fairly general in that the space dependent system matrix functions as well as the boundary conditions may switch in time. For the case in which the switching occurs between hyperbolic systems in the canonical diagonal form, we provide two sets of sufficient conditions for the switched system to be exponentially stable under arbitrary switching signals. These results are generalizations of the corresponding results for the un-switched case. Furthermore, we provide an explicit dwell-time bound on the switching signals that guarantee exponential stability of the switched system under the assumption that each of the individual systems are stable. Our results of stability under arbitrary switching generalize to the case in which switching occurs between non-diagonal hyperbolic systems that are diagonalizable using a common transformation. For the case in which no such transformation exists, we prove existence of a dwell-time bound on the switching signals such that exponential stability is guaranteed.

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• HTML

  Saurabh Amin, Falk Hante, Alexandre Bayen. <a
  href="http://chess.eecs.berkeley.edu/pubs/454.html"
  ><i>Exponential stability of switched hyperbolic
  systems in a bounded domain</i></a>, Technical
  report,  UC Berkeley, 2008.

• Plain text

  Saurabh Amin, Falk Hante, Alexandre Bayen. "Exponential
  stability of switched hyperbolic systems in a bounded
  domain". Technical report,  UC Berkeley, 2008.

• BibTeX

  @techreport{AminHanteBayen08_ExponentialStabilityOfSwitchedHyperbolicSystemsInBounded,
      author = {Saurabh Amin and Falk Hante and Alexandre Bayen},
      title = {Exponential stability of switched hyperbolic
                systems in a bounded domain},
      institution = {UC Berkeley},
      year = {2008},
      abstract = {We consider switching in time among a finite
                family of systems governed by linear hyperbolic
                partial differential equations on a bounded space
                interval. The switching system is fairly general
                in that the space dependent system matrix
                functions as well as the boundary conditions may
                switch in time. For the case in which the
                switching occurs between hyperbolic systems in the
                canonical diagonal form, we provide two sets of
                sufficient conditions for the switched system to
                be exponentially stable under arbitrary switching
                signals. These results are generalizations of the
                corresponding results for the un-switched case.
                Furthermore, we provide an explicit dwell-time
                bound on the switching signals that guarantee
                exponential stability of the switched system under
                the assumption that each of the individual systems
                are stable. Our results of stability under
                arbitrary switching generalize to the case in
                which switching occurs between non-diagonal
                hyperbolic systems that are diagonalizable using a
                common transformation. For the case in which no
                such transformation exists, we prove existence of
                a dwell-time bound on the switching signals such
                that exponential stability is guaranteed. },
      URL = {http://chess.eecs.berkeley.edu/pubs/454.html}
  }
  

Posted by Saurabh Amin on 23 Jun 2008.
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