In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-
state stability (ISS) for infinite-dimensional systems. This property allows for the estimation of …

This paper is concerned with boundary dissipative conditions that guarantee the exponential
stability of classical solutions of one-dimensional quasi-linear hyperbolic systems. We …

Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on
pairs of counter-convecting (“heterodirectional”) transport PDEs with distributed local …

In this work, we consider the problem of boundary stabilization for a quasilinear 2\times2
system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with …

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 consider the problem of boundary stabilization and state estimation for a 2× 2 system of
first-order hyperbolic linear PDEs with spatially varying coefficients. First, we design a full …

This paper deals with the problem of boundary stabilization of first-order n*n
inhomogeneous quasi-linear hyperbolic systems. A backstep** method is developed. The …

We solve the problem of stabilizing a general class of linear first-order hyperbolic systems.
Considered systems feature an arbitrary number of coupled transport PDEs convecting in …

This paper is devoted to a simple and new proof on the optimal finite control time for general
linear coupled hyperbolic system by using boundary feedback on one side. The feedback …

We address the problem of adaptive output-feedback stabilization of general first-order
hyperbolic partial integro-differential equations (PIDE). Such systems are also referred to as …