Ali Saberi

TL;DR: The existence of linear state feedback and/or output feedback control laws for semi-global exponential stabilization rather than global asymptotic stabilization of linear time-invariant systems was shown in this article.

TL;DR: The authors take a semiglobal approach to solve some of the central control problems for linear systems with saturating actuators, including stabilization, input-additive disturbance rejection, and robust stabilization in the presence of matched nonlinear uncertainties.

TL;DR: In this paper, a special coordinate basis for multivariable linear systems is introduced, which can be used to express the fundamental properties of linear systems regarding controllability (stabiliza-bility), observability (detectability), invariant zero, decoupling zero, infinite zero structure etc.

TL;DR: In this book the output regulation problem is examined in depth, new, highly significant dimensions are added to the problem and all pertinent topics associated with it are discussed.

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.