160 research outputs found
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 L∞, 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 L∞ are equivalent
On continuity of solutions for parabolic control systems and input-to-state stability
We study minimal conditions under which mild solutions of linear evolutionary
control systems are continuous for arbitrary bounded input functions. This
question naturally appears when working with boundary controlled, linear
partial differential equations. Here, we focus on parabolic equations which
allow for operator-theoretic methods such as the holomorphic functional
calculus. Moreover, we investigate stronger conditions than continuity leading
to input-to-state stability with respect to Orlicz spaces. This also implies
that the notions of input-to-state stability and integral-input-to-state
stability coincide if additionally the uncontrolled equation is dissipative and
the input space is finite-dimensional.Comment: 19 pages, final version of preprint, Prop. 6 and Thm 7 have been
generalised to arbitrary Banach spaces, the assumption of boundedness of the
semigroup in Thm 10 could be droppe
Input-to-state stability of unbounded bilinear control systems
We study input-to-state stability of bilinear control systems with possibly
unbounded control operators. Natural sufficient conditions for integral
input-to-state stability are given. The obtained results are applied to a
bilinearly controlled Fokker-Planck equation.Comment: 20 pages, completely new version based on the few preliminary ideas
in v1. Compared to v1, the results have been significantly generalized and
extende
Input-to-State Stability with Respect to Boundary Disturbances for a Class of Semi-linear Parabolic Equations
This paper studies the input-to-state stability (ISS) properties based on the
method of Lyapunov functionals for a class of semi-linear parabolic partial
differential equations (PDEs) with respect to boundary disturbances. In order
to avoid the appearance of time derivatives of the disturbances in ISS
estimates, some technical inequalities are first developed, which allow
directly dealing with the boundary conditions and establishing the ISS based on
the method of Lyapunov functionals. The well-posedness analysis of the
considered problem is carried out and the conditions for ISS are derived. Two
examples are used to illustrate the application of the developed result.Comment: Manuscript submitted to Automatic
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