@TechReport{	  it:2015-013,
  author	= {Torbj{\"o}rn Wigren},
  title		= {Constraints in nonlinear $\mathcal{L}_2$-stable networked
		  control},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Systems and Control},
  year		= {2015},
  number	= {2015-013},
  month		= may,
  abstract	= {The report derives a robust networked controller design
		  method for systems with saturation where the delay is large
		  and unknown, as in unidirectional flow-control. A classical
		  linear robust criterion is first formulated in terms of the
		  sensitivity- and complementary sensitivity functions. Based
		  on the Popov-criterion a new asymptotic constraint is
		  derived, which specifies the minimum amount of low
		  frequency gain in the sensitivity function, to guarantee
		  non-linear closed loop $\mathcal{L}_2$-stability. This
		  result guides the selection of the design criterion,
		  thereby adjusting the linear controller design for better
		  handling of delay and saturation. The controller design
		  method then uses gridding to pre-compute the
		  $\mathcal{L}_2$ stability region. Based on the pre-computed
		  stability region, a robust $\mathcal{L}_2$-stable
		  controller can be selected. Alternatively, an adaptive
		  controller could recompute $\mathcal{L}_2$-stable
		  controllers on-line using the pre-computed stability
		  region. Simulations show that the controller meets the
		  specified stability and performance requirements.}
}