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 show that the existence of a non-coercive Lyapunov function is sufficient for uniform
global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances …

Since the seminal work of Russell and Weiss in 1994, resolvent conditions for various
notions of admissibility, observability and controllability, and for various notions of linear …

This work contributes to the recently intensified study of input-to-state stability for infinite-
dimensional systems. The focus is laid on the relation between input-to-state stability and …

The main purpose of this paper is to treat semigroup properties like norm continuity,
compactness and differentiability for perturbed semigroups in Banach spaces. In particular …

We derive conditions for well-posedness of semilinear evolution equations with unbounded
input operators. Based on this, we provide sufficient conditions for such properties of the flow …

In the first part of this article we introduce the notion of a backward–forward conditioning
(BFC) system that generalises the notion of zero-class admissibility introduced in Xu et …

We derive conditions for well-posedness of semilinear evolution equations with unbounded
input operators and the corresponding boundary control systems. Based on this, we provide …

In this paper we discuss the characteristic property of the left invertible semigroups on
general Banach spaces and admissibility of the observation operators for such semigroups …

In natural sciences one often has a great interest to describe motions in time mathematically.
This interest can be traced back to Galileo Galilei (1564-1642), and way beyond him, who …