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- W2069718736 abstract "It is an established fact that systems which have transfer matrices with poles converging to the imaginary axis cannot have exponentially stable time responses. Recently it was proved that for a class of partial differential equations with such a structure of poles it is possible to have a fast decay in time, uniformly in space, as arbitrary polynomials if the initial conditions are smooth enough and with an appropriate decay at infinity. The non-homogeneous version of this result which we present here can be summarized as follows: 'arbitrary regularity in space of the input function leads to arbitrary polynomial convergence in time towards the steady state'. The relation between the properties of the input function and the rate of convergence of the poles to the imaginary axis is quantitative and we indicate methods for computing this rate. We also provide conditions for exponential stability in this context. Due to some limitations in exponential stabilization by feedback a natural alternative to stabil..." @default.
- W2069718736 created "2016-06-24" @default.
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- W2069718736 date "2001-01-01" @default.
- W2069718736 modified "2023-10-14" @default.
- W2069718736 title "Input-output stability degrees for undamped constant coefficients linear partial differential equations" @default.
- W2069718736 doi "https://doi.org/10.1080/00207170010010533" @default.
- W2069718736 hasPublicationYear "2001" @default.
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