Semi-uniform input-to-state stability of infinite-dimensional systems
We introduce the notions of semi-uniform input-to-state stability and its subclass, polynomial input-to-state stability, for infinite-dimensional systems. We establish a characterization of semi-uniform input-to-state stability based on attractivity properties as in the uniform case. Sufficient cond...
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| Veröffentlicht in: | Mathematics of control, signals, and systems signals, and systems, 2022-12, Vol.34 (4), p.789-817 |
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| creator | Wakaiki, Masashi |
| description | We introduce the notions of semi-uniform input-to-state stability and its subclass, polynomial input-to-state stability, for infinite-dimensional systems. We establish a characterization of semi-uniform input-to-state stability based on attractivity properties as in the uniform case. Sufficient conditions for linear systems to be polynomially input-to-state stable are provided, which restrict the range of the input operator depending on the rate of polynomial decay of the product of the semigroup and the resolvent of its generator. We also show that a class of bilinear systems are polynomially integral input-to-state stable under a certain smoothness assumption on nonlinear operators. |
| doi_str_mv | 10.1007/s00498-022-00326-1 |
| format | Article |
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| subjects | Communications Engineering Control Decay rate Dimensional stability Linear systems Mathematics Mathematics and Statistics Mechatronics Networks Operators (mathematics) Ordinary differential equations Original Article Partial differential equations Polynomials Robotics Smoothness System theory Systems Theory |
| title | Semi-uniform input-to-state stability of infinite-dimensional systems |
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