Relaxed Conditions for the Exponential Stability of a Class of Linear Time-Varying Systems

This technical note states new sufficient conditions for the exponential stability of linear time-varying (LTV) systems of the form aeligmacr(ldr) =A(t)aelig(t). The approach proposed derives and uses the notion of perturbed frozen time (PFT) form that can be associated to any LTV system. Exploiting the Bellman-Gronwall lemma, relaxed stability conditions are then stated in terms of ldquoaveragerdquo parameter variations. Salient features of the approach are: pointwise stability of A(ldr) is not required, ||Amacr(ldr)|| may not be bounded, the stability conditions also apply to uncertain systems. The approach is illustrated by numerical examples.