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Ponencia
Explicit boundary control of a reaction-diffusion equation on a disk
(Elsevier, 2014)
This paper introduces an explicit full-state boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on a disk. The backstepping method is used to design the control law. ...
Artículo
Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs
(Institute of Electrical and Electronics Engineers (IEEE), 2016)
Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on pairs of counter-convecting (“heterodirectional”) transport PDEs with distributed local coupling and with controls at one or both ...
Artículo
Explicit output-feedback boundary control of reaction-diffusion PDEs on arbitrary-dimensional balls
(Société de Mathématiques Appliquées et Industrielles (SMAI), 2016)
This paper introduces an explicit output-feedback boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an n-ball (which in 2-D reduces to a disk and in 3-D reduces ...
Ponencia
Boundary control of a singular reaction-diffusion equation on a disk
(Elsevier, 2016)
Recently, the problem of boundary stabilization for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However, ...
Ponencia
Local exponential H2 stabilization of a 2x2 quasilinear hyperbolic system using backstepping
(Institute of Electrical and Electronics Engineers (IEEE), 2011)
We consider the problem of boundary stabilization for a quasilinear 2×2 system of first-order hyperbolic PDEs. We design a full-state feedback control law, with actuation on only one end of the domain, and prove local H 2 ...
Ponencia
Backstepping stabilization of an underactuated 3 X 3 linear hyperbolic system of fluid flow transport equations
(Institute of Electrical and Electronics Engineers (IEEE), 2012)
We investigate the boundary stabilization of a particular subset of 3×3 linear hyperbolic systems with varying coefficients on a bounded domain. The system is underactuated since only one of the three hyperbolic PDEs is ...
Artículo
Boundary Control of Coupled Reaction-Advection-Diffusion Systems with Spatially-Varying Coefficients
(Institute of Electrical and Electronics Engineers (IEEE), 2016)
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with ...
Artículo
Marcum Q-functions and explicit kernels for stabilization of 2×2 linear hyperbolic systems with constant coefficients
(Elsevier, 2014)
We find the exact analytical solution to a Goursat PDE system governing the kernels of a backstepping-based boundary control law that stabilizes a constant-coefficient 2×2 system of first-order hyperbolic linear PDEs. The ...
Ponencia
Bilateral boundary control of one-dimensional first- and second-order PDEs using infinite-dimensional backstepping
(Institute of Electrical and Electronics Engineers (IEEE), 2016)
This paper develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with an ...
Artículo
Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping
(Society for Industrial and Applied Mathematics, 2013)
In this work, we consider the problem of boundary stabilization for a quasilinear 2 × 2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, ...