Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases
Identifieur interne : 003660 ( Istex/Curation ); précédent : 003659; suivant : 003661Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases
Auteurs : Antoine Chaillet [France] ; Yacine Chitour [France] ; Antonio Loría [France] ; Mario Sigalotti [France]Source :
- Mathematics of Control, Signals, and Systems [ 0932-4194 ] ; 2008-06-01.
English descriptors
Abstract
Abstract: Consider the controlled system dx/dt = Ax + α(t)Bu where the pair (A, B) is stabilizable and α(t) takes values in [0, 1] and is persistently exciting, i.e., there exist two positive constants μ, T such that, for every t ≥ 0, $${\int_t^{t+T}\alpha(s){\rm d}s \geq \mu}$$ . In particular, when α(t) becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback u = Kx, with K only depending on (A, B) and possibly on μ, T, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when A is neutrally stable and when the system is the double integrator.
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DOI: 10.1007/s00498-008-0024-1
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level="j">Mathematics of Control, Signals, and Systems</title><title level="j" type="abbrev">Math. Control Signals Syst.</title><idno type="ISSN">0932-4194</idno><idno type="eISSN">1435-568X</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>London</pubPlace><date type="published" when="2008-06-01">2008-06-01</date><biblScope unit="volume">20</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="135">135</biblScope><biblScope unit="page" to="156">156</biblScope></imprint><idno type="ISSN">0932-4194</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0932-4194</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Persistency of excitation</term><term>Stabilization</term><term>Switching systems</term><term>Time-varying linear systems</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Consider the controlled system dx/dt = Ax + α(t)Bu where the pair (A, B) is stabilizable and α(t) takes values in [0, 1] and is persistently exciting, i.e., there exist two positive constants μ, T such that, for every t ≥ 0, $${\int_t^{t+T}\alpha(s){\rm d}s \geq \mu}$$ . In particular, when α(t) becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback u = Kx, with K only depending on (A, B) and possibly on μ, T, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when A is neutrally stable and when the system is the double integrator.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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