Date of download: 10/19/2017 Copyright © ASME. All rights reserved. From: Input-Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows Appl. Mech. Rev. 2009;62(2):020803-020803-27. doi:10.1115/1.3077635 Figure Legend: The controlled Ginzburg–Landau equation with stochastic excitation: (a) White noise w with zero mean and unit variance W=1 forces the system at x=−11, just upstream of unstable region with input B1 as a Gaussian function (green). Measurements y(t) of the state (red Gaussian) contaminated by white noise with zero mean and variance G=0.1 are taken at xs=0. The actuator u with control penalty R=1 is placed upstream of the sensor at xu=−3. The rms values of the uncontrolled and LQG-controlled state are given by the solid red and black lines, respectively. The absolute value of the state |q| is shown in an x-t-plane in (b), while the lower plot (c) displays the kinetic energy E=‖q‖M as a function of time. The control is only engaged for t∊[250,750]. Dashed lines in (c) indicate the mean value computed from Lyapunov equation.