Global stabilization of feedforward systems with exponentially unstable Jacobian linearization

The global stabilization of a class of feedforward systems having an exponentially unstable Jacobian linearization is achieved by a high-gain feedback saturated at a low level. The control law forces the derivatives of the state variables to small values along the closed-loop trajectories. This "slow control" design is illustrated with a benchmark example and its limitations are emphasized. © 1999 Elsevier Science B.V. All rights reserved.

Lyapunov functions for stable cascades and applications to global stabilization

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems, one of which is stable rather than asymptotically stable. A new cross-term construction in the Lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition. This method is instrumental in the global stabilization of feedforward systems, and new stabilization results are derived from the generalized construction.

Some remarks about periodic feedback stabilization

Periodic feedback stabilization is a very natural solution to overcome the topological obstructions which may occur when one tries to asymptotically (locally) stabilize a (locally) controllable nonlinear system around an equilibrium point. The object of this paper is to give a simple geometric interpretation of this fact, to show that one obtains a weakened form of those obstructions when periodic feedback is used, and to illustrate the success of periodic feedback stabilization on a representative system which contains a drift.

Carbonating magnesia for soil stabilization

This paper investigates the potential for carbonating reactive magnesia (MgO) to serve as a more sustainable soil stabilization method by providing rapid and significant strength development of the stabilized soil through absorbing substantial quantities of CO2. Gaseous CO2 was forced through laboratory-prepared reactive MgO-treated soil samples in a triaxial cell set-up, and their resulting mechanical and microstructural properties were investigated using unconfined compressive strength, X-ray diffraction, and scanning electron microscopy. The results showed that adequately carbonated MgO-treated soils could, in a few hours, reach a similar strength range to corresponding 28 day Portland cement (PC)-stabilized soils. Hydrated magnesium carbonates, namely nesquehonite and hydromagnesite-dypingite, were the main products of the carbonated MgO in the soil, and were responsible for the significant strength development.