Remarks on computing the ℋ2 norm of incompressible fluids using descriptor state-space formulation

Rashad Moarref, Mihailo Jovanovic

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper utilizes descriptor state-space formulation for computation of energy amplification in incompressible channel flows. The dynamics of velocity and pressure fluctuations in these flows are described by a system of partial differential-algebraic equations. Typically, the evolution model is obtained by projecting the velocity fluctuations on a divergence-free subspace which eliminates pressure from the equations. This procedure results into a standard state-space representation and the problem of quantifying receptivity of velocity fluctuations to stochastic exogenous disturbances is solved using well-known ℋ2 formalism. In this paper, however, it is shown how energy amplification can be computed directly from the original system of the linearized Navier-Stokes and continuity equations. This approach avoids the need for finding the evolution model which is advantageous in many applications.

Original languageEnglish (US)
Title of host publication2008 American Control Conference, ACC
Number of pages6
StatePublished - Sep 30 2008
Event2008 American Control Conference, ACC - Seattle, WA, United States
Duration: Jun 11 2008Jun 13 2008


Other2008 American Control Conference, ACC
Country/TerritoryUnited States
CitySeattle, WA


  • Descriptor systems
  • Distributed systems
  • Incompressible fluids
  • Navier-Stokes equations
  • ℋ norm


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