7 papers
Stabilization of 1D Linear Hyperbolic Balance Laws by Integral Difference Control and Application to Networks Stabilization
Adam Braun, Jean Auriol, Lucas Brivadis
This paper develops a unified method for the exponential stabilization of first-order linear hyperbolic balance laws under general actuation, including both underactuated boundary…
Stabilization of Integral Difference Equations by Solving a Corona Problem
Adam Braun, Jean Auriol, Lucas Brivadis
This paper proposes a stabilizing state-feedback control law for vector-valued state systems with a scalar control input, governed by a general class of integral difference equatio…
Stabilization of a chain of 3 hyperbolic PDEs with 2 inputs in arbitrary position
Adam Braun, Jean Auriol, Lucas Brivadis
This paper addresses the stabilization of a chain of three coupled hyperbolic partial differential equations actuated by two control inputs applied at arbitrary nodes of the networ…
A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation
Adam Braun, Lucas Brivadis, Jean Auriol
We propose an observer design for a cascaded system composed of an arbitrary nonlinear ordinary differential equation (ODE) with a 1D heat equation. The nonlinear output of the ODE…
A superposition approach for the ISS Lyapunov-Krasovskii theorem with pointwise dissipation
Andrii Mironchenko, Fabian Wirth, Antoine Chaillet +1
We show that the existence of a Lyapunov-Krasovskii functional (LKF) with pointwise dissipation (i.e. dissipation in terms of the current solution norm) suffices for input-to-state…
A Spectral Exponential Stability Criterion for Integral Difference Equations and Delay Differential Equations in various state spaces
Adam Braun, Jean Auriol, Lucas Brivadis
It is well-known that the exponential stability of Integral Difference Equations and Delay Difference Equations, in the usual state space of continuous functions, is equivalent to…