Ignored input dynamics and a new characterization of control Lyapunov functions

Our objective in this paper is to extend as much as possible the dissipativity approach for the study of robustness of stability in the presence of known/unknown but ignored input dynamics. This leads us to: give a new characterization of control Lyapunov functions (CLF) where L_fV is upper-bounded by a function of L_gV,; define the dissipativity approach as : - assuming the ignored dynamics are dissipative with storage function W and (known) supply rate w, - analyzing closed-loop stability with the sum of the storage function W and a CLF for the nominal part. Stability margin is given in terms of an inequality the supply rate should satisfy. Unfortunately this extension of the dissipativity approach cannot still cope with ignored dynamics which have non zero relative degree or are non minimum phase.