Constraints in Nonlinear L 2 - Stable Networked Control ⋆

The paper 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 sensitivityand 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 L2-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 L2 stability region. Based on the precomputed stability region, a robust L2-stable controller can be selected. Alternatively, an adaptive controller could recompute L2-stable controllers on-line using the pre-computed stability region. Simulations show that the controller meets the specified stability and performance requirements.