In the well-known nonlinear system reference
H.Khalil, Nonlinear Systems Third Edition
in chapter 13.Feedback linearization, Khalil developed a theory for feedback linearization(Theorem 13.2)
Does this theorem also implies state controllability of nonlinear systems in the form of x_dot=f(x)+g(x)*u?
In this theorem first asumptions implies controllability of system.
Proof of this condition is shown for example in: Hunt, L.R., “Sufficient Conditions for Controllability”, IEEE Trans. Circuit and Systems, May 1982.
Dear Maciej Rozewicz
thank you for your answer and introducing the reference
I have read the reference and it seems that the first assumption in the theorem 13.2 of Khalils book is not a sufficient condition , beacuse in the paper in corollary 3.4 it is said that besides the first assumption in theorem 13.2 of khalils book, g1,..gm should be linearly independent and there exist a point that f (x) is tangent to integral manifold of g1,..,gm
Dear Ali Namadchian
In theorem 13.2, from Khalils book, system with single-input is considered, so there is no problem with independence of g_i vectors.
Moreover in this paper: Article Observability and Controllability of Nonlinear Networks: The...
authors presented this condition (section II.C) as sufficient conditionfor local controllability.
Dear Maciej Rozewicz
you are right, Khalil theorem is for single control input systems.
beside controllability , is there a method to compute reachability set for non-linear affine systems?
Pls follow this reference. I think it will be very helpful to you for all above.
NONLINEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
Lu, Sun, Mei. KLUWER ACADEMIC PUBLISHERS.
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