Sufficient Conditions for the Exponential Stability of Linear Systems Subject to Norm Bounded, Bounded Rate Uncertainties

In this paper we consider a linear system subject to norm bounded, time-varying uncertainties. Necessary and sufficient conditions for quadratic stability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees uniform exponential stability in presence of arbitrarely time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time. The contribution of this paper is that of giving a sufficient condition for the exponential stability of the system taking into account the bound on the rate of variation of the uncertainties; therefore such condition will result a less conservative analysis tool than the quadratic stability approach