Immersion and invariance (I2): A new tool in nonlinear control design

A new method to design asymptotically stabilizing control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the construction used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. Applications of the general theory to the stabilization of systems in triangular form and in feedforward form are also discussed. Finally, the application of the proposed theory to an adaptive vision problem, which is an example of an adaptive control problem for nonlinearly parameterized systems, is reported.