Global Uniform Asymptotic Stability of Cascaded Non-autonomous Non-linear Systems: Application to Stabilisation of a Diesel Engine

摘要

In ihis paper we deal with the stability analysis problem of cascaded non-autonomous non-linear systems. In particular, we answer to the following quesiions (i) What happens with the solutions of a time-varying non-linear system which is globally uniformly stable (GUS), when it is periurbed by the output of a globally exponentially stable (GES) sys- tem, in particular, when both systems form a cas- cade? (ii) If a time-varying non-linear system is globally uniformly asymptotically stable (GUAS), is this stability properly preserved when it is perturbed by an exponentially decaying input? Our proofs are based on a standard `delta-epsilon Lyapunov analysis. Finally, we show the utility of our results by applying our theorems to the problem of stabilis- ation of a turbo-charged diesel engine.