Small-gain theorem for a class of abstract parabolic systems

We consider a class of abstract control system of parabolic type with observation which the state, input and output spaces are Hilbert spaces. The state space operator is assumed to generate a linear exponentially stable analytic semigroup. An observation and control action are allowed to be describ...

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Published in:Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica Vol. 38; no. 5; pp. 651 - 680
Main Author: Grabowski, Piotr
Format: Journal Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2018
Subjects:
control of infinite-dimensional systems
infinite-time LQ-control problem
Lur'e feedback systems
semigroups
ISSN:1232-9274
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Abstract We consider a class of abstract control system of parabolic type with observation which the state, input and output spaces are Hilbert spaces. The state space operator is assumed to generate a linear exponentially stable analytic semigroup. An observation and control action are allowed to be described by unbounded operators. It is assumed that the observation operator is admissible but the control operator may be not. Such a system is controlled in a feedback loop by a controller with static characteristic being a globally Lipschitz map from the space of outputs into the space of controls. Our main interest is to obtain a perturbation theorem of the small-gain-type which guarantees that null equilibrium of the closed-loop system will be globally asymptotically stable in Lyapunov's sense.
AbstractList We consider a class of abstract control system of parabolic type with observation which the state, input and output spaces are Hilbert spaces. The state space operator is assumed to generate a linear exponentially stable analytic semigroup. An observation and control action are allowed to be described by unbounded operators. It is assumed that the observation operator is admissible but the control operator may be not. Such a system is controlled in a feedback loop by a controller with static characteristic being a globally Lipschitz map from the space of outputs into the space of controls. Our main interest is to obtain a perturbation theorem of the small-gain-type which guarantees that null equilibrium of the closed-loop system will be globally asymptotically stable in Lyapunov's sense.
Author Grabowski, Piotr
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Snippet We consider a class of abstract control system of parabolic type with observation which the state, input and output spaces are Hilbert spaces. The state space...
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SubjectTerms control of infinite-dimensional systems
infinite-time LQ-control problem
Lur'e feedback systems
semigroups
Title Small-gain theorem for a class of abstract parabolic systems
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