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… 
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147 Citations
Highly Influential Citations
4
Background Citations
53
Methods Citations
21
Results Citations
4

147 Citations

Input-to-state stability and integral input-to-state stability of non-autonomous infinite-dimensional systems
  • H. Damak
  • Mathematics
    Int. J. Syst. Sci.
  • 2021
TLDR
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
TLDR
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
TLDR
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
Construction of Lyapunov Functions for Interconnected Parabolic Systems: An iISS Approach
TLDR
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
Non-coercive Lyapunov functions for input-to-state stability of infinite-dimensional systems
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
  • J. Schmid, H. Zwart
  • Mathematics
    ESAIM: 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
Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces
...
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References

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TLDR
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Input-to-state stability of impulsive and switching hybrid systems with time-delay
Converse Lyapunov Theorem of Input-to-State Stability for Time-delay Systems
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