On the existence of stabilising feedback controls for real analytic small-time locally controllable systems

Mathematics of Control, Signals and Systems - Tập 27 - Trang 467-492 - 2015
Pantelis Isaiah1
1Faculty of Aerospace Engineering, The Technion—Israel Institute of Technology, Haifa, Israel

Tóm tắt

It is shown that, for real analytic control systems of the form $$f:{M}\times \varOmega \ni (q,u)\mapsto f(q,u)\in {T}_q{M}$$ , where M is a real analytic manifold and $$\varOmega $$ is a separable metric space, small-time local controllability from an equilibrium $$p\in {M}$$ implies the existence of a piecewise analytic feedback control that locally stabilises f at p. The proof is similar in spirit to an earlier analogous result for globally controllable systems; however, it resolves several technical obstructions that emerge when the assumption of small-time local controllability is substituted for that of global controllability. In the light of a recent characterisation of small-time local controllability for homogeneous control systems, the main result of the paper implies that, for a large class of control systems that appear in applications and the literature, there is a computable sufficient condition for stabilisability by means of a piecewise analytic feedback control.

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