On the stabilization of some nonlinear control systems: results, tools, and applications

It has been proved by Brockett that, contrary to the case of linear control systems, many controllable nonlinear control systems cannot be stabilized by means of stationary continuous feedback laws. In this paper we give results showing that many controllable nonlinear control systems can be stabilized by means of time-varying continuous feedback laws and that many controllable and observable nonlinear control systems can be stabilized by means of time-varying dynamic continuous feedback laws. We show the interest of time-varying feedback laws for robustness with respect to measurement disturbances. We also present methods to design stabilizing feedback laws and we give applications to satellites and fluid mechanics.

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