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 …

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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 …

This paper provides conditions that guarantee existence and uniqueness of classical
solutions for a non-local conservation law on a ring road with possible nudging (or 'look …

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 time-invariant finite-dimensional systems, it is known that global asymptotic stability
(GAS) is equivalent to uniform GAS (UGAS), in which the decay rate and transient overshoot …

In this paper, we provide Lyapunov-based tools to establish input-to-state stability (ISS) and
integral input-to-state stability (iISS) for non-autonomous infinite-dimensional systems. We …

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 …