This chapter reviews the challenges for the extension of the Input-to-State Stability (ISS)
property for systems described by Partial Differential Equations (PDEs). The methodologies …

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 …

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

This paper deals with an event-triggered boundary control of constant-parameters reaction–
diffusion PDE systems. The approach relies on the emulation of backstepping control along …

Motivated by vibration control of a mining cable elevator avoiding frequent actions of a
massive actuator, which is a hydraulic cylinder driving a head sheave, we present an event …

This paper deals with the stability analysis of a system of finite dimension coupled to a
vectorial transport equation. We develop here a new method to study the stability of such a …

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This paper deals with the problem of boundary stabilization of first-order n*n
inhomogeneous quasi-linear hyperbolic systems. A backstepping 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 …

We detail in this article the development of a delay-robust stabilizing state feedback control
law for an underactuated network of two subsystems of heterodirectional linear first-order …