Partial differential equations (PDEs) are the most elegant way to model the dynamics of not
only much of the physical world around us but, increasingly, many of the social systems we …

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional
control systems. We show that for certain classes of admissible inputs, the existence of an …

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 …

A family of time-varying hyperbolic systems of balance laws is considered. The partial
differential equations of this family can be stabilized by selecting suitable boundary …

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 …

For one-dimensional parabolic partial differential equations with disturbances at both
boundaries and distributed disturbances we provide input-to-state stability (ISS) estimates in …

For bilinear infinite-dimensional dynamical systems, we show the equivalence between
uniform global asymptotic stability and integral input-to-state stability. We provide two proofs …

This note addresses input-to-state stability (ISS) properties with respect to (wrt) boundary
and in-domain disturbances for Burgers' equation. The developed approach is a …