32 research outputs found
Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback
We use the backstepping method to study the stabilization of a 1-D linear
transport equation on the interval (0, L), by controlling the scalar amplitude
of a piecewise regular function of the space variable in the source term. We
prove that if the system is controllable in a periodic Sobolev space of order
greater than 1, then the system can be stabilized exponentially in that space
and, for any given decay rate, we give an explicit feedback law that achieves
that decay rate
Two sided boundary stabilization of two linear hyperbolic PDEs in minimum time
International audience— We solve the problem of stabilizing two coupled linear hyperbolic PDEs using actuation at both boundary of the spatial domain in minimum time. We design a novel Fredholm transformation similarly to backstepping approaches. This yields an explicit full-state feedback law that achieves the theoretical lower bound for convergence time to zero
Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback
We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized exponentially in that space and, for any given decay rate, we give an explicit feedback law that achieves that decay rate
Finite-time internal stabilization of a linear 1-D transport equation
We consider a 1-D linear transport equation on the interval (0, L), with an internal scalar control. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized in finite time, and we give an explicit feedback law
Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space
In this article we are interested in the boundary stabilization in finite
time of one-dimensional linear hyperbolic balance laws with coefficients
depending on time and space. We extend the so called "backstepping method" by
introducing appropriate time-dependent integral transformations in order to map
our initial system to a new one which has desired stability properties. The
kernels of the integral transformations involved are solutions to non standard
multi-dimensional hyperbolic PDEs, where the time dependence introduces several
new difficulties in the treatment of their well-posedness. This work
generalizes previous results of the literature, where only time-independent
systems were considered
Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback
We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized exponentially in that space and, for any given decay rate, we give an explicit feedback law that achieves that decay rate
Finite-time internal stabilization of a linear 1-D transport equation
We consider a 1-D linear transport equation on the interval (0, L), with an internal scalar control. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized in finite time, and we give an explicit feedback law