# Stabilization of a system of n+1 coupled first-order hyperbolic linear PDEs with a single boundary input

Authors: F. Di Meglio , R. Vazquez , M. Krstic, IEEE transactions on Automatic Control, Vol 58, no 12, pp. 3097 - 3111, December 2013 DOI: 10.1109/TAC.2013.2274723

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and one leftward convecting transport PDE. We design a controller, which requires a single control input applied on the leftward convecting PDE's right boundary, and an observer, which employs a single sensor on the same PDE's left boundary. We prove exponential stability of the origin of the resulting plant-observer-controller system in the spatial L2-sense.

BibTeX:

@Article{2017-04-01,

author = {R. Vazquez F. Di Meglio, M. Krstic},

title = {Stabilization of a system of n+1 coupled first-order hyperbolic linear PDEs with a single boundary input},

journal = {IEEE transactions on Automatic Control},

volume = {58},

number = {12},

pages = {3097 - 3111},

year = {2013},

}

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and one leftward convecting transport PDE. We design a controller, which requires a single control input applied on the leftward convecting PDE's right boundary, and an observer, which employs a single sensor on the same PDE's left boundary. We prove exponential stability of the origin of the resulting plant-observer-controller system in the spatial L2-sense.

BibTeX:

@Article{2017-04-01,

author = {R. Vazquez F. Di Meglio, M. Krstic},

title = {Stabilization of a system of n+1 coupled first-order hyperbolic linear PDEs with a single boundary input},

journal = {IEEE transactions on Automatic Control},

volume = {58},

number = {12},

pages = {3097 - 3111},

year = {2013},

}