Petar V. Kokotovic

TL;DR: A new adaptive nonlinear control design which achieves a complete controller-identifier separation and is more flexible than the Lyapunov-based design because the identifier can employ any standard update law gradient and least-squares, normalized and unnormalized.

TL;DR: In this article, a singular perturbation approach is used to unify a class of classical and recent results on high-gain systems and to show their relationships with multivariable transmission zero analysis, cheap control problems, and sliding mode in variable structure systems.

TL;DR: In this article, conditions for complete separation of slow and fast regulator designs are formulated and a second order approximation of the optimal performance is achieved without the knowledge of the small singular perturbation parameter.

TL;DR: A robust recursive design technique is developed for uncertain nonlinear plants in vectorial strict feedback form that bridges the geometric design with the speed assignment.

Abstract: A linear stabilizable, nonlinear asymptotically stable, cascade system is globally stabilizable by smooth dynamic state feedback if (a) the linear subsystem is right invertible and weakly minimum phase, and, (b) the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output. Both of these conditions are coordinate-free and there is freedom of choice for the linear output variable. This result generalizes several earlier sufficient conditions for stabilizability. Moreover, the weak minimum-phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem.