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 …

We prove characterizations of input-to-state stability (ISS) for a large class of infinite-
dimensional control systems, including some classes of evolution equations over Banach …

Due to unbounded input operators in partial differential equations (PDEs) with boundary
inputs, there has been a long-held intuition that input-to-state stability (ISS) properties and …

In this work, the relation between input-to-state stability and integral input-to-state stability is
studied for linear infinite-dimensional systems with an unbounded control operator. Although …

We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this
class the significance of noncoercive Lyapunov functions is analyzed. It is shown that the …

We introduce a monotonicity-based method for studying input-to-state stability (ISS) of
nonlinear parabolic equations with boundary inputs. We first show that a monotone control …

We show that a nonlinear locally uniformly asymptotically stable infinite-dimensional system
is automatically locally input-to-state stable (LISS) provided the nonlinearity possesses …

A reaction–diffusion–advection equation with uncertain parameters, and additionally subject
to disturbances of both matched and mismatched nature, is considered. It is assumed that …

Input-to-state stability (ISS) for systems described by partial differential equations has seen
intensified research activity recently, and in particular the class of boundary control systems …