Felix L. Schwenninger

Infinite-Dimensional Input-to-State Stability and Orlicz Spaces

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 a special focus is laid on the case

On input-to-state-stability and integral input-to-state-stability for parabolic boundary control systems

L^{\infty}

Less than one implies zero

, general function spaces are considered for the inputs. We show that integral input-to-state stability can be characterized in terms of input-to-state stability with respect to Orlicz spaces. Since we consider linear systems, the results can also be formulated in terms of admissibility. For parabolic diagonal systems with scalar inputs, both stability notions with respect to

Strong input-to-state stability for infinite-dimensional linear systems

L^\infty

Generators with a closure relation

are equivalent.

Functional calculus estimates for Tadmor–Ritt operators

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 integral input-to-state stability for linear systems with a possibly unbounded control operator. The main result is that for parabolic diagonal systems both notions coincide, even in the setting of inputs in L∞, and a simple criterion is derived.

On functional calculus estimates

In this paper we show that from an estimate of the form supt≥0 C(t) - cos(at)I < 1, we can conclude that C(t) equals cos(at)I. Here (C(t)) t≥0 is a strongly continuous cosine family on a Banach space.

Functional Calculus for C_0-semigroups Using Infinite-dimensional Systems Theory

This paper deals with strong versions of input-to-state stability for infinite-dimensional linear systems with an unbounded control operator. We show that strong input-to-state stability with respect to inputs in an Orlicz space is a sufficient condition for a system to be strongly integral input-to-state stable with respect to bounded inputs. In contrast to the special case of systems with exponentially stable semigroup, the converse fails in general.

Zero-two law for cosine families

Assume that a block operator of the form

On continuity of solutions for parabolic control systems and input-to-state stability

\left(\begin{array}{c}A_1\\ A_2\ 0\end{array}\right)