# Input-to-state stability of infinite-dimensional control systems

@article{Dashkovskiy2013InputtostateSO, title={Input-to-state stability of infinite-dimensional control systems}, author={Sergey Dashkovskiy and Andrii Mironchenko}, journal={Mathematics of Control, Signals, and Systems}, year={2013}, volume={25}, pages={1-35} }

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 ISS-Lyapunov function implies the ISS of a system. Then for the case of systems described by abstract equations in Banach spaces, we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a…

## 147 Citations

Input-to-state stability and integral input-to-state stability of non-autonomous infinite-dimensional systems

- MathematicsInt. J. Syst. Sci.
- 2021

It is proved that for a class of admissible inputs the existence of an ISS Lyapunov function implies the ISS of a system in Banach spaces and it is shown that uniform global asymptotic stability is equivalent to their integral input-to-state stability for non-autonomous generalised bilinear systems overBanach spaces.

Input-to-State Stability of Nonlinear Impulsive Systems

- MathematicsSIAM J. Control. Optim.
- 2013

It is proved that impulsive systems, which possess an input-to-state stable (ISS) Lyapunov function, are ISS for time sequences satisfying the fixed dwell-time condition and two small-gain theorems are proved that provide a construction of an ISS Lyap unov function for an interconnection of impulsive Systems if the ISS LyAPunov functions for subsystems are known.

Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions

- MathematicsSIAM Rev.
- 2020

This survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems and motivates the study of ISS property for distributed parameter systems.

Lyapunov functions for input-to-state stability of infinite-dimensional systems with integrable inputs

- Mathematics
- 2020

Construction of Lyapunov Functions for Interconnected Parabolic Systems: An iISS Approach

- MathematicsSIAM J. Control. Optim.
- 2015

Stability of two highly nonlinear reaction-diffusion systems is established by the the proposed small-gain criterion, and for interconnections of partial differential equations, the choice of a right state and input spaces is crucial.

ISS small-gain criteria for infinite networks with linear gain functions

- MathematicsSyst. Control. Lett.
- 2021

Non-coercive Lyapunov functions for input-to-state stability of infinite-dimensional systems

- Mathematics
- 2019

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 existence of…

Stabilization of port-Hamiltonian systems by nonlinear boundary control in the presence of disturbances

- MathematicsESAIM: Control, Optimisation and Calculus of Variations
- 2021

In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order N ∈ ℕ on a bounded 1-dimensional spatial domain (a, b). In order to achieve stabilization,…

Stability conditions for infinite networks of nonlinear systems and their application for stabilization

- MathematicsAutom.
- 2020

Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces

- MathematicsSyst. Control. Lett.
- 2018

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