The Byrnes-Isidori form with respect to the relative degree is studied for time-varying linear multi-input, multi-output systems. It is clarified in which sense this form is a normal form. (A,B)-invariant time-varying subspaces are defined and the maximal (A,B)-invariant time-varying subspace included in the kernel of C is characterized. This is exploited to characterize the zero dynamics of th...

In the present work, we study autocatalytic pathways which contain reactions that need the use of one of their own productions. These pathways are common in biology; one of the simplest and widely studied autocatalytic pathways is Glycolysis. This pathway produces energy by breaking down Glucose. It is shown that this pathway can be simplified as a network of three biochemical reactions. We fir...

This work concerns general multiple-input/multiple-output (MIMO) nonlinear systems with nonsingular characteristic matrix. For these systems, the problem of inversion is revisited and explicit formulas are derived for the full-order and the reduced inverse system. The reduced inverse naturally leads to an explicit calculation of the unforced zero dynamics of the system and the definition of a c...

As a complement to some new breakthroughs on global almost disturbance decoupling problem with stability for nonlinear systems, in a recent note, we identiied a class of unstable zero dynamics that are allowed to be aaected by disturbances. The class of the unstable zero dynamics identiied in that note is linear and have all the poles at the origin. In this paper, we enlarge such a class of zer...

The zero dynamics of a hybrid model of bipedal walking are introduced and studied for a class of N-link, planar robots with one degree of underactuation and outputs that depend only on the configuration variables. Asymptotically stable solutions of the zero dynamics correspond to asymptotically stabilizable orbits of the full hybrid model of the walker. The Poincaré map of the zero dynamics is ...

This paper concerns the problem of output consensus in nonlinear non-minimum phase systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, an output redefinition method is proposed. The new outputs of agents are functions of original outputs and internal states and defined such that the dynamics of agents a...

We discuss the effect of zero-temperature attenuation, which has been recently observed in spin dynamics of spin-polarized Fermi liquids, on other Fermi-liquid processes. The transfer of" this attenuation mechanism J?om transverse spin dynamics to longitudinal processes can be caused by the magnetic dipole interaction, namely, by the direct dipole processes and the dipole coupling between the t...