Analysis and synthesis of nonlinear control systems
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In this dissertation, regular nonlinear control systems of the form .x=X0(x)+[sigma]spi=1m uiXi(x) are considered. Necessary and sufficient conditions are given for a point to be reached from one of its entire neighborhoods in finite time by a piece-wise analytic feedback controller. Under such a feedback controller, the domain of attraction of the point is maximal. In particular, necessary and sufficient conditions on stabilization of a point or a periodic orbit in two dimension flat space are given. Moreover, practical examples are discussed and some interesting results are derived. Finally, when one dimensional systems are considered, precise criteria for control, stabilization, and existence of invariant sets under large disturbances are given.