@inbook{cb83193fea3e46aeb4e8f571ddbc09d1,
title = "LMI-based H∞ -boundary control of nonsmooth parabolic and hyperbolic systems",
abstract = "This chapter develops, in side-by-side fashion, exponential stability analysis and L2 -gain analysis via the Lyapunov method for scalar uncertain distributed parameter systems, governed by nonsmooth partial differential equations of the parabolic and hyperbolic types. The nonsmooth uncertainties are admitted to be time-, space-, and state-dependent, with a priori known upper and lower bounds. Sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities for both systems. These conditions are then utilized to synthesize L2 -static output-feedback boundary controllers of the systems in question. Numerical examples illustrate the efficacy of the method.",
keywords = "Boundary control, Boundary sensing, Disturbance attenuation, Semilinear hyperbolic system, Semilinear parabolic system",
author = "Orlov, {Yury V.} and Aguilar, {Luis T.}",
note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media, New York.",
year = "2014",
doi = "10.1007/978-1-4939-0292-7_7",
language = "Ingl{\'e}s",
series = "Systems and Control: Foundations and Applications",
publisher = "Birkhauser",
number = "9781493902910",
pages = "105--120",
booktitle = "Systems and Control",
edition = "9781493902910",
}