Semiglobal stabilization of a boundary controlled viscous Burgers´ equation

In this paper we describe our recent results on the use of a proportional error boundary feedback control law to render a closed loop Burgers´ system semiglobally exponentially stable. This result is proven in detail in our recent work which also contains a nonlinear enhancement of classical root-locus methodology for a nonlinear distributed parameter system. Our exponential stabilization result holds in the spaces L², H¹ and L^∞. We also showed previously that the resulting closed loop system is “practically semiglobally stabilizable” in L²-norm