Global uniform asymptotic stability of cascaded non-autonomous non-linear systems:: Application to stabilisation of a diesel engine

In this paper we deal with the stability analysis problem of cascaded non-autonomous non-linear systems. In particular, we answer to the following questions: (i) What happens with the solutions of a time-varying non-linear system which is globally uniformly stable (GUS), when it is perturbed by the output of a globally exponentially stable (GES) system, in particular, when both systems form a cascade? (ii) If a time-varying non-linear system is globally uniformly asymptotically stable (GUAS), is this stability properly presented 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 stabilisation of a turbo-charged diesel engine.