We consider stabilization of an affine in control, nonlinear autonomous hybrid dynamical system (HDS) plant model. HDS are systems that combine the dynamics of a discrete system abstractly modeled as an automaton and continuous system modeled as nonlinear ordinary differential equations. We drive a HDS version of exact linearization via nonlinear feedback. In doing so we were able to bypass the issue of characterization of inherent switching boundaries in the plant model to derive stabilizing controllers.
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