dc.contributor.author Isaiah, Pantelis dc.contributor.other Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) en dc.date 2012-09-24 10:24:22.51 en dc.date.accessioned 2012-09-25T21:23:53Z dc.date.available 2012-09-25T21:23:53Z dc.date.issued 2012-09-25 dc.identifier.uri http://hdl.handle.net/1974/7506 dc.description Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-09-24 10:24:22.51 en dc.description.abstract Controllability and stabilisability are two fundamental properties of control systems and it is intuitively appealing to conjecture that the former should imply the latter; especially so when the state of a control system is assumed to be known at every time instant. Such an implication can, indeed, be proven for certain types of controllability and stabilisability, and certain classes of control systems. In the present thesis, we consider real analytic control systems of the form $\Sgr:\dot{x}=f(x,u)$, with $x$ in a real analytic manifold and $u$ in a separable metric space, and we show that, under mild technical assumptions, small-time local controllability from an equilibrium $p$ of \Sgr\ implies the existence of a piecewise analytic feedback \Fscr\ that asymptotically stabilises \Sgr\ at $p$. As a corollary to this result, we show that nonlinear control systems with controllable unstable dynamics and stable uncontrollable dynamics are feedback stabilisable, extending, thus, a classical result of linear control theory. en_US Next, we modify the proof of the existence of \Fscr\ to show stabilisability of small-time locally controllable systems in finite time, at the expense of obtaining a closed-loop system that may not be Lyapunov stable. Having established stabilisability in finite time, we proceed to prove a converse-Lyapunov theorem. If \Fscr\ is a piecewise analytic feedback that stabilises a small-time locally controllable system \mbox{$\Sgr:\dot{x}=f(x,u)$} in finite time, then the Lyapunov function we construct has the interesting property of being differentiable along every trajectory of the closed-loop system obtained by applying" \Fscr\ to \Sgr. We conclude this thesis with a number of open problems related to the stabilisability of nonlinear control systems, along with a number of examples from the literature that hint at potentially fruitful lines of future research in the area. dc.language en en dc.language.iso en en_US dc.relation.ispartofseries Canadian theses en dc.rights This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner. en dc.subject Feedback Stabilisation en_US dc.subject Geometric Control Theory en_US dc.title Feedback Stabilisation of Locally Controllable Systems en_US dc.type thesis en_US dc.description.degree Ph.D en dc.contributor.supervisor Lewis, Andrew D. en dc.contributor.department Mathematics and Statistics en
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