On l∞ and l2 robustness of spatially invariant systems

Azeem Sarwar, Petros G. Voulgaris, Srinivasa M. Salapaka

Research output: Contribution to journalArticlepeer-review


We consider spatiotemporal systems and study their l∞ and l 2 robustness properties in the presence of spatiotemporal perturbations. In particular, we consider spatially invariant nominal models and provide necessary and sufficient conditions for system robustness for the cases when the underlying perturbations are linear spatiotemporal varying, and nonlinear spatiotemporal invariant, unstructured or structured. It turns out that these conditions are analogous to the scaled small gain condition (which is equivalent to a spectral radius condition and a linear matrix inequality for the l∞ and l2 cases, respectively) derived for standard linear time-invariant models subject to time-varying linear and time-invariant nonlinear perturbations.

Original languageEnglish (US)
Pages (from-to)607-622
Number of pages16
JournalInternational Journal of Robust and Nonlinear Control
Issue number6
StatePublished - Apr 2010


  • Distributed
  • L
  • L∞
  • Robustness analysis
  • Spatially invariant

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Chemical Engineering
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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