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 …

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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 …

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 …

This paper studies the input-to-state stability (ISS) properties for a class of semi-linear
parabolic partial differential equations (PDEs) with respect to boundary disturbances. In …

We consider infinite heterogeneous networks, consisting of input-to-state stable subsystems
of possibly infinite dimension. We show that the network is input-to-state stable, provided …

For a broad class of infinite-dimensional systems, we characterize input-to-state practical
stability (ISpS) using the uniform limit property and in terms of input-to-state stability. We …

We prove that input-to-state stability (ISS) of nonlinear systems over Banach spaces is
equivalent to existence of a coercive Lipschitz continuous ISS Lyapunov function for this …